Google Interview Riddle - 3 Friends Bike and Walk || Logic and Math Puzzle

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  • เผยแพร่เมื่อ 21 ก.ย. 2024
  • Google interview puzzle :
    Three brothers Alex, Bob and Carl travel to visit their uncle who lives exactly 300 kms away from their house, to celeberate his birthday.
    They have a motorbike (bike) which can carry a maximum of two persons at a time.
    Assume that the bike has a constant speed of 60 km/hr.
    Each brother can walk at a speed of 15 km/hr.
    The brothers are brilliant logicians, just like you.
    If, they all start from their house at the same time.
    what is the shortest possible time in which they all can reach their destination.
    Pause the video and think logically.
    It's an amazing Google interview riddle to challenge your intelligence.
    So if you are looking for a job at Google, please study optimization based puzzles in detail.
    You can share puzzles and riddles with me on these links:
    Gmail : logicreloaded@gmail.com
    Facebook(message) : / mohammmedammar
    Also try these brilliant mind blowing puzzles:
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ความคิดเห็น • 1.9K

  • @angirasnazar59
    @angirasnazar59 3 ปีที่แล้ว +2862

    In India , it doesn't matter what the capacity of a bike is , people adjust themselves anyhow 😂😂😂

  • @MysticIndie
    @MysticIndie 3 ปีที่แล้ว +363

    Bob is going to win Gold medal in next Olympics by walking 86 km at 15 km/hr. 🥇

    • @L4ki0
      @L4ki0 3 ปีที่แล้ว +14

      You got me laughning very well.
      Also Carl too - same distance for same amount of time.
      Like i said: this is not logical because nobody can walk 15 km/hr

    • @motijewelsghatkoparw8516
      @motijewelsghatkoparw8516 3 ปีที่แล้ว +4

      Meanwhile Usain bolt -37km/hr world record

    • @decryptic999
      @decryptic999 3 ปีที่แล้ว +6

      @@motijewelsghatkoparw8516 That's his top speed, right. But it is for a short period of time (sprinting).
      Usain Bolt sprint was 100m in 9.58s.
      Now if we want to see him do this for 53.57km...
      53.57km = 53570m
      53570m / 100m * 9.58s = 5132s = 85.53min = 1.425h
      That would be 1 hours and 25.5 minutes where he needs to sprint at his top speed.

    • @CodingWithAmin
      @CodingWithAmin 3 ปีที่แล้ว +2

      😂😂😂 we better reduce the distanc from 300 on to 30 km 😉

    • @Anonymous-nd9cp
      @Anonymous-nd9cp 3 ปีที่แล้ว

      And he won

  • @utsavkumarvats1192
    @utsavkumarvats1192 3 ปีที่แล้ว +2317

    The one riding bike never walked 😂😂he Is real genius

    • @muthukannur7149
      @muthukannur7149 3 ปีที่แล้ว +18

      You are not understood the question

    • @MKD1101
      @MKD1101 3 ปีที่แล้ว +20

      @@muthukannur7149 have*

    • @kishorevenugopal6191
      @kishorevenugopal6191 3 ปีที่แล้ว +45

      He's the interviewer 😂

    • @devondevon4366
      @devondevon4366 3 ปีที่แล้ว +31

      He could walk, but he would have to get off real fast (such as within a second) and let the other brother ride (then he walks) such as if his first stop is at the 71.428 km mark to return to pick up the other brother behind. In this case, all three would meet up at the 100km mark.
      If the bike stops at the 71.428 km mark when Alex was the rider (Alex and Bob on the bike) then that would take 1.19 hours (71.428 divided by 60). At the same, Carl would be at the 17.857 km mark( 1.19 at 15 miles per hour). So after 1.19 hours, they are just 53.571 km apart ( 71.428 - 17.857). Bob could return at 60 km/hr to get Carl who is walking at 15 km/hr while Alex continues to also walk at 15 km/hr. Bob and Carl would meet in 0.71428 seconds (53.571 divided by 75 since traveling in OPPOSITE DIRECTION add 60 +15) at the 28.57 km mark (17.857 + 10.7142) while Alex is at the 82.1422 km mark (71.428 + 10.7142, the 10.714 comes from multiplying 15 by 0.71428 hours). Now
      they are still 53.571 km apart, but this time traveling in the SAME DIRECTION and will meet up after traveling for 71.428 km (53.571 x 4/3, the '4' is the 60 miles per hour and '3' is 45 miles from substracting 60-15, so the 4/3 ratio)). But since Bob and Carl are at the 28.57 km mark
      and will meet up with Alex after 71.428 km of traveling they will meet up at the 100 km mark (71.428 + 28.57). Note the 3 times (1.19 then 0.71428 then 1.19) or 1.19 + 0.71428 + 1.19 = 3.09428 hrs just to reach the 100km but since the trip is 300 km, just multiply 3.09428 by 3 to get 9.28284 hours or about 9 hours 17 minutes.
      How did I get 71.428? I came up with a formula and reduce it to just dividing 100 km where all three would meet after the bike return by 1.4. So in this case, since I want them to meet at 100km I divide the 100 km mark by 1.4 to get 71.428. If you want all three to meet up at 50 km just divide 50 by 1.4. In other words, the time it took them to meet up at the 50 km mark, they would just need to multiply that time by 6 since 6 times 50=300km

    • @aruljebin
      @aruljebin 3 ปีที่แล้ว +16

      @@devondevon4366 you have some patience

  • @FoodFFacts
    @FoodFFacts 3 ปีที่แล้ว +310

    Everyone : Calculate how many hours
    Me : who the hell able to walk 15km/hr

    • @eestitulevik-et-eestitegij5436
      @eestitulevik-et-eestitegij5436 3 ปีที่แล้ว +2

      Same haha

    • @juliankneaz6893
      @juliankneaz6893 3 ปีที่แล้ว +2

      @@eestitulevik-et-eestitegij5436 and for so many hours

    • @erishkigal1
      @erishkigal1 3 ปีที่แล้ว +1

      it's just a brisky walk/stroll

    • @b99andla
      @b99andla 3 ปีที่แล้ว +6

      @@erishkigal1 Could you please film yourself strolling at 15km/hr?

    • @erishkigal1
      @erishkigal1 3 ปีที่แล้ว +1

      @@b99andla damn, you're right - I was sure it was pace: 15min/km

  • @saurabh1627kondkar
    @saurabh1627kondkar 3 ปีที่แล้ว +867

    this is how i carry my two friends on a bike while in blue zone in pubg...

  • @jensraab2902
    @jensraab2902 3 ปีที่แล้ว +25

    I took a slightly modified approach that of course yields the same results but is, I think, less confusing as it requires only one unknown and is perhaps a little more intuitive.
    The basic idea is very similar to the one of the video: the "biking brother" carries one of the "walking brothers" some distance, drops him off, and returns to the point which the other "walking brother" has reached, picks him up and drives again towards the uncle's house where all of them arrive simultaneously.
    The "trick" is to realize that the first walking brother walks a distance x before he's carried the remaining way to the uncle, while the second walker is first carried on motorbike and then walks the rest - but since they must both spend the same time walking and going on motorbike respectively in order to arrive at the uncle's house, the distance where the second walker is dropped off is the same distance x that the first walker goes before being picked up.
    So, for both walkers the following equation is true:
    t = x / v₁ + (s-x) / v₂; x being the unknown partial distance, s being the total distance (i.e. the 300 km), and v₁ and v₂ the velocities of the walking and riding the motorbike respectively
    I habitually approach problems with the general case and plug in the specific numbers later. The downside, I know, is that plugging in the numbers first might speed up the solution but the upside is that one gets a solution that is valid for *all* cases - different numbers? --> you just plug in different values at the very end! ;-)
    Back to the problem. Let's now focus on the lucky bastard who doesn't have to walk at all.
    He will first cover the total distance s minus the partial distance x where he drops off the first brother. When he goes back, the other brother's already walked partial distance x and the go the remainder all the way to the uncle, i.e. also (s - x).
    What about the bit when he's going the other way after having dropped of the first brother to pick up the second? This is the total distance s with the partial distance x missing on both ends, i.e. (s-2x).
    In total, the biker goes (s-x)+(s-2x)+(s-x) = (3s-4x).
    Going with motorbike speed, he'll need the following time for this:
    t = (3s-4x) / v₂
    These two expressions must be equivalent and therefore:
    x / v₁ + (s-x) / v₂ = (3s-4x) / v₂
    We perform, I quote, "simple calculation" and plug in the numbers to learn that x is 600/7 km and t is 9 ²/₇ h.
    OK, that last line was a bit facetious. It is easier to plug in the numbers first but if one continues with the general case one finds that the partial distance x is:
    x = 2sv₁ / (v₂ + 3v₁)
    and the time to reach the uncle's house is:
    t = s/v₂ * [3 - 8 / (v₂/v₁ + 3)]
    Like I said above, the beauty of these general solutions is that they will work for any value of the given parameters.

  • @ashutoshsharma3953
    @ashutoshsharma3953 3 ปีที่แล้ว +1698

    Uncle :- Why you guys are late?
    3 Fellows :- Actually we are wasting time in equating a way to reach in less time.
    Edit :- I think I have a good humour that I make 1k+ people laugh.

    • @haonguyentuan4019
      @haonguyentuan4019 3 ปีที่แล้ว +17

      There no way the waste 90 min doing that

    • @ScientistMaya
      @ScientistMaya 3 ปีที่แล้ว +5

      Lol😂

    • @techtalks2948
      @techtalks2948 3 ปีที่แล้ว +2

      😂

    • @joshuaklein8429
      @joshuaklein8429 3 ปีที่แล้ว +21

      The basic solution comes out to 11 hours, so since it is unlikely it would take more than 1h43m to come up with a more optimized solution, it would be worth considering. That’s a little post hoc though, since you wouldn’t know it’s worth it until after calculating it, and it doesn’t account for making two people walk for ~2.5 hours each. Still, it’s the same principle as sharpening the axe for 5 minutes to chop a tree in 1 minute versus chopping for 10 minutes.

    • @n4nivilmathew
      @n4nivilmathew 3 ปีที่แล้ว

      🤣

  • @shahriarhussain2366
    @shahriarhussain2366 3 ปีที่แล้ว +194

    Legends say:
    They never reached their uncle's house as they are still trying to solve the complex equation.
    😂

    • @gunmun2005
      @gunmun2005 3 ปีที่แล้ว +1

      🤣oh boi

    • @ejrupp9555
      @ejrupp9555 2 ปีที่แล้ว

      Because Bob only went 299.99 km ... Bob couldn't finish the last 10 meters with his math.

    • @robinhammond4446
      @robinhammond4446 ปีที่แล้ว

      Xeno's other Dilemma.

    • @942WAxeO
      @942WAxeO ปีที่แล้ว

      🤣

  • @sivapradeep977
    @sivapradeep977 3 ปีที่แล้ว +1073

    Ultra optimised solution:
    Call their uncle to the brothers house
    Then it would take only 5hrs😂😂😂

    • @subashsahu8925
      @subashsahu8925 3 ปีที่แล้ว +12

      No man..then time will be indefinite...

    • @justsomerandomweeb4243
      @justsomerandomweeb4243 3 ปีที่แล้ว +24

      @@subashsahu8925 no if uncle use 100kmh car

    • @vanshofficial599
      @vanshofficial599 3 ปีที่แล้ว +5

      @Chor Narendra Modi 😂😂

    • @siddharthdyavanapalli4617
      @siddharthdyavanapalli4617 3 ปีที่แล้ว +1

      Yeah🤣🤣🤣 but uncle is very very busy

    • @painterken2542
      @painterken2542 3 ปีที่แล้ว +11

      Your hired with promotion..were fireing this guy that's wasting everyone's time with over complications

  • @rocketfrog3143
    @rocketfrog3143 ปีที่แล้ว +10

    I did it this way in my head:
    Once I figured out that to maximize efficiency, all 3 brothers needed to arrive at the same time, and that meant the "walking" brothers each had to walk (and ride) the same distance, I called the walking distance "X". The dropoff point is X from the destination, and when the biker returns to the pickup point, it will be X from the origin. The distance in between the pickup and dropoff is "Y".
    The entire distance can be split in three sections: X -> Y -> X
    Now the question is: how far is X and Y? To figure it out, we can compare how far the brothers go in the same time period; from the start until the original walker is picked up by the rider.
    One brother walks distance X to the pickup in the time that the biker goes X+Y to the dropoff, then Y again back to the pickup, or X+2Y.
    We know that riding is 4x as fast as walking (60km/h) / (15km/h), so if the walker went X, he would have gone 4X, had he been riding.
    We know that the distance the rider went, and the distance the walker would have went if he were riding, are equal
    Therefore the equation is X+2Y=4X
    reduce to Y=1.5X
    The distance from origin to destination can now be rewritten as a ratio: 1:1.5:1 (from X:Y:X)
    To use integers for ease, double it to 2:3:2
    This splits the total distance into sevenths, X is 2/7 of the total distance, and Y is 3/7 of the total distance
    So the "walking" brothers walk 2/7 of the way and ride 5/7 of the way
    The rider rides 5/7 of the way (X+Y), drops off his brother, rides back 3/7 of the way (Y), picks up the other brother, and rides 5/7 of the way to the origin, for a total of:
    5/7 + 3/7 + 5/7 = 13/7
    The rider rode 13/7 of the total distance, which was 300km, or 300*13/7=557 & 1/7km
    557 1/7km @ 60km/h = 9 2/7 hours
    No complex equations or calculations required. I'm curious, how easy was it to follow my solution?

  • @JonathanSpencer12
    @JonathanSpencer12 3 ปีที่แล้ว +427

    ***Alternative solution***
    We know optimal solution involves a drop off and a pick up. Let x, y, and z be time to first drop off, time between drop off and pick up, and time until finish.
    Eqn1: 15(x+y) + 60z = 300 (distance of initial walker)
    Eqn2: 60x + 15(y+z) = 300 (distance of initial passenger)
    Eqn3: 60(x - y + z) = 300 (distance traveled by motorcycle, has to backtrack so y is negative)
    3 equations, 3 unknowns, no problem.
    Eqn1 + Eqn2 + 2*Eqn3 -> x + z = 50/7
    Sub that solution back into Eqn3 and find y = 15/7
    Total time elapsed
    x + y + z = 65/7 = 9.28

    • @kartikgupta6695
      @kartikgupta6695 3 ปีที่แล้ว +9

      Gr8 solution simple and fast

    • @Thelegendarian-
      @Thelegendarian- 3 ปีที่แล้ว +3

      A bit hard

    • @palashagrawal2343
      @palashagrawal2343 3 ปีที่แล้ว +11

      nothing extraordinary he used distance as variable and u used times as that and yeah which surely gives u the right ans

    • @Thelegendarian-
      @Thelegendarian- 3 ปีที่แล้ว +2

      @@palashagrawal2343 sorry but i am a lower classes to calcualte this eqn

    • @ThatControlUser
      @ThatControlUser 3 ปีที่แล้ว +6

      @@Thelegendarian- what? This is basic stuff. How can this be hard?

  • @Rahul_Hindu_Mondal_108
    @Rahul_Hindu_Mondal_108 3 ปีที่แล้ว +362

    Meanwhile in *INDIA* :
    ALEX SITTING ON TANKER OF BIKE
    BOB DRIVING
    CARL SITTING IN BACK

    • @prashantmishra5070
      @prashantmishra5070 3 ปีที่แล้ว +3

      Sure 🤣🤣

    • @mrzia3032
      @mrzia3032 3 ปีที่แล้ว +6

      Yhi hota h😂🤣

    • @mirekkowalski796
      @mirekkowalski796 3 ปีที่แล้ว +5

      And they are taking one hitchhiker with big backpack on their way.

    • @MrK0091
      @MrK0091 3 ปีที่แล้ว +5

      And sining "ye dosti...."

    • @FarhanAhmed-qx7ko
      @FarhanAhmed-qx7ko 3 ปีที่แล้ว +2

      Abe agar car hi tha to bike ki jarurat hi kya, sab milkar car me ja sakte the. This not wastage of time, this is wastage of fuel LOL

  • @riankardison
    @riankardison 3 ปีที่แล้ว +364

    Bob doesn't wasting time. He would be cleaning their uncle's house while waiting for the other 2. Their uncle would gives bob some money to buy fuel for their motorcycle. Everyone is happy now

  • @314159265352
    @314159265352 3 ปีที่แล้ว +270

    If they are brothers in their teens, they will fight for who will go on bike first and end up all three walking dragging their bike along.

    • @lohithashwa6653
      @lohithashwa6653 3 ปีที่แล้ว +9

      And then arises the problem as to who should drag the bike.

    • @Hans-gb4mv
      @Hans-gb4mv 3 ปีที่แล้ว +1

      Would they still be able to keep their speed of 15kph if they do that? If not, shouldn't they just leave the bike behind?

    • @uberfu
      @uberfu 3 ปีที่แล้ว +1

      Or Carl gets stuck on the handlebars.

    • @uberfu
      @uberfu 3 ปีที่แล้ว

      @@lohithashwa6653 The youngest brother - that's easy.

    • @omerakarca6456
      @omerakarca6456 3 ปีที่แล้ว

      I also thought about that and a more fair solution would be like this
      They will solve the problem as it is 100km and and in each 100km someone else will go with bike
      You can calculate it is the same result

  • @md.afzalbari4890
    @md.afzalbari4890 3 ปีที่แล้ว +273

    First i get the ans - 11 hrs and then i know the correct approach to solve this. Thanks man👍

    • @LOGICALLYYOURS
      @LOGICALLYYOURS  3 ปีที่แล้ว +15

      Well done!

    • @sanjibkumar9025
      @sanjibkumar9025 3 ปีที่แล้ว +1

      Me too

    • @ans7452
      @ans7452 3 ปีที่แล้ว +1

      Same here....

    • @sbxsurya3438
      @sbxsurya3438 3 ปีที่แล้ว +9

      ARE BHAIYA AGAR TUM IS QUESTION KO SOLVE KARLETE TO ISKA COMMENT NAHI KAR RAHE HOTE BALKI TUM 20 LACK SALARY KE SAATH MAST GOOGLE ME KAM KAR RAHE HOTE SAMJHE.

    • @mohammadzafeer2610
      @mohammadzafeer2610 3 ปีที่แล้ว +1

      @@sbxsurya3438 😂😂😂

  • @jgoemat
    @jgoemat 3 ปีที่แล้ว +5

    I took the easy route. I figured out what would happen if Alex dropped Bob off at the 300km mark in 5 hours and let him keep walking. Carl moved 75km and is 225km from the 300km mark. As Alex moves back to pick up Carl they will be moving towards each other at 75km/h and will meet in 3 hours at the 120km mark, and Bob moved another 45km so he's at 345km. Now Alex and Carl have to catch up to Bob at 45 km/h relative speed and he is 225 km away so that's another 5 hours. They all end up at the 420km mark in 13 hours so no matter the distance using this arrangement their average speed will be 420/13 km/h. 420km/300km is 7/5, so they could get to 300km in (13*5)/7 hours, or ~9.29 hours

  • @Victor-ev3vu
    @Victor-ev3vu 3 ปีที่แล้ว +430

    What if uncle isn't at home😂.They all will waste time

  • @random1110111
    @random1110111 3 ปีที่แล้ว +49

    “Simple calculation”
    Maybe when I was in year 10.
    As an engineer 20 years on. No chance

    • @Marque734
      @Marque734 3 ปีที่แล้ว +2

      He made it overly complicated

  • @AdilAmanullah
    @AdilAmanullah 3 ปีที่แล้ว +159

    Imagine the calculations goes wrong and Bob arrives a month later

  • @vladschiopu2885
    @vladschiopu2885 3 ปีที่แล้ว +204

    So we basically have 3 walking Usain Bolts that never get tired, and they have a weird motorcycle that reach 60km/h instantly, but can't go faster

    • @anandasatria7734
      @anandasatria7734 3 ปีที่แล้ว +9

      Walking Usain Bolt? They can accelerate to 15kmph in no time! Usain Bolt couldn't do that!

    • @wiono
      @wiono 3 ปีที่แล้ว +2

      50 cc scooter

    • @anandasatria7734
      @anandasatria7734 3 ปีที่แล้ว +1

      @@wiono Good point.

    • @ashleygarvin7177
      @ashleygarvin7177 3 ปีที่แล้ว +1

      With no firctional costs for dismounting, changing directions or changing passengers

    • @sumer9999
      @sumer9999 3 ปีที่แล้ว +2

      Those who are not interested in maths, comment like this

  • @auzanwidhatama9421
    @auzanwidhatama9421 3 ปีที่แล้ว +25

    "All brothers are brilliant logicians" then let them solve their own problem themselves lol

    • @ejrupp9555
      @ejrupp9555 2 ปีที่แล้ว +1

      That was my thought ... why do they need my help. I'll optimize my time by helping someone else.

  • @chetansurve
    @chetansurve 3 ปีที่แล้ว +50

    We must also add the time taken to solve the problem in final answer😂

    • @matthewsmith8573
      @matthewsmith8573 3 ปีที่แล้ว +2

      They can start off immediately. That gives Bob (they're all brilliant logicians, so any of them could figure it out) a few hours while he's the passenger to figure out where he should get dropped off. Though if I were Bob I'd be tempted to adjust the numbers so that I wouldn't have to walk/sprint quite so fast. To make it a little more fair, Alex and Bob should trade places once they catch up to Carl again.

  • @chiragahjolia
    @chiragahjolia 3 ปีที่แล้ว +52

    I lived this puzzle way back during 2001 to 2003; where I used to drop my Mom-Dad to bus-stop from home. And Always used to follow this approach. During this commute, I suddenly thought of finding the exact point where I can drop the first one and then pick the second one.
    First I worked on this lot and found the answer and then identified the formula as well.
    Then, I shared that puzzle with many friends many times; but none appeared with correct answer so far. Then I decided to make a video on that, but that time never came and you got my thoughts ;)

    • @LOGICALLYYOURS
      @LOGICALLYYOURS  3 ปีที่แล้ว +7

      Lovely !!!! Solving a real life problem gives you much higher confidence and satisfaction than solving a puzzle in theory.

    • @TheRandomizerYT
      @TheRandomizerYT 3 ปีที่แล้ว +1

      @@LOGICALLYYOURS
      Yes... Nice

    • @indianbot0077
      @indianbot0077 3 ปีที่แล้ว

      Ur story is incredible 😁

    • @mageshm3997
      @mageshm3997 8 หลายเดือนก่อน +1

      But your mom and dad probably had different walking speed and its useless if the distance to cover is short.

    • @chiragahjolia
      @chiragahjolia 8 หลายเดือนก่อน +2

      @@mageshm3997 It was just situation that I shared, and out of which I imagine the format of puzzle. Also the distance was not that short, more than 10 km (i guess)

  • @rich_moorly
    @rich_moorly 3 ปีที่แล้ว +1

    I did it simpler with less variables. Actually just 1.
    1. We understand, that all 3 must move all the time.
    2. We understand, that bike must be running all the time.
    3. Alex is a biker and will be always driving.
    4. Bob and Carl will need to take part of way by bike and part by feet.
    5. Since Bob's and Carl's walking speed is the same we can state, that proportion of walking and driving for them is the same.
    6. X is the point, where Alex will drop Bob.
    7. Bob will be (300-x)km traveling by bike with speed 60km/h and (x)km traveling be feet with speed 15km/h
    8. Carl will start from traveling (x)km by feet with speed 15km/h and then (300-x)km by bike.
    9. Alex will travel (300-x) to Bob drop point, then (300-2x) to Carl pickup point and again (300-x)
    10. Time for Alex=((300-x)+(300-2x)+(300-x))/60= *(900-4x)/60*
    11. The same time for Bob/Carl = (300-x)/60+x/15= *(300+3x)/60*
    12. Now T=T and 900-4x=300+3x, so x=600/7= *85.7 km* , so *T=9.28 h*

  • @slidergrey
    @slidergrey 3 ปีที่แล้ว +163

    More than 5 hours and half "to walk" at a speed of 15 km/h ... WOW! Google employs supermen.

    • @aleksandertrubin4869
      @aleksandertrubin4869 3 ปีที่แล้ว +5

      From information I could find it is actually normal speed for professional ultramaraphon runners: current record for 5-7hr run seems to be in 100km distance: just above 6hr (meaning 16-17km/hr)
      Although it seems like for amateur 6hr runner 10km/hr is more realistic (but still would require significant prior training)

    • @archwaldo
      @archwaldo 3 ปีที่แล้ว +8

      @@aleksandertrubin4869 "walking" bruh.

    • @kriparane6370
      @kriparane6370 3 ปีที่แล้ว +4

      Walking speed couldn't be 15 kmph it would running speed

    • @mirekkowalski796
      @mirekkowalski796 3 ปีที่แล้ว +5

      If I could walk that fast I would have never bought a bike with 60km/h limit.

    • @mirekkowalski796
      @mirekkowalski796 3 ปีที่แล้ว +5

      @@kriparane6370 Well the world record in sports walking on distance 50km is 3h32m so it's pretty close to 15km/h (more than 14km/h). Yet I doubt if Carl or Bob are olimpic medalists in that discipline.

  • @grgr6720
    @grgr6720 3 ปีที่แล้ว +6

    My solution gave 11 hours and it took me 2 mins. I am still happy with the accuracy/ efficiency ratio 😁😁

  • @AMTechnicalOfficial
    @AMTechnicalOfficial 3 ปีที่แล้ว +69

    That animation and your explanation is very awesome 🥰 Thanks man for the Video 😘

    • @LOGICALLYYOURS
      @LOGICALLYYOURS  3 ปีที่แล้ว +8

      Thanks bro for the appreciation :)

  • @midnighttrain-jz2my
    @midnighttrain-jz2my 2 หลายเดือนก่อน

    Actually, the shortest time can be found, without calculating any distances, explicitly. Lets say:
    T0: time, when the first guy is dropped off the bike,
    T1: time, which this guy needs to get to the destination,
    T2: time, for the bike to get back to the third guy, who is already walking toward the destination,
    T3: time, for the two guys on bike to get to the destination.
    As you said, they all arrive at the same time. We have the following equations:
    a) 60 T0 +15 T1 = 300 (the dropped-off guy)
    b) 15 T0 +15 T2 + 60 T3 = 300 (the picked-up guy)
    c) 60 T0 - 60 T2 + 60 T3 = 300 (the bike-guy),
    d) T1 = T2 + T3 (simultaneous arrival)
    4 equations, can be solved for T0..3, to obtain the total shortest time: T = T0 + T1 ~ 9,28 h

  • @subhammondal3796
    @subhammondal3796 3 ปีที่แล้ว +33

    Amazing! Amazing! Awesome puzzle 🤯🤯🤯first I thought I cracekd it but when I saw the sloution I just say 'Mind blowing' !!

  • @walex996
    @walex996 3 ปีที่แล้ว +6

    More precisely, It's 9 hours, 16 minutes, 8 seconds.
    Awesome video, brother.
    loved the explanation & animations.

    • @Atook774
      @Atook774 3 ปีที่แล้ว +1

      No
      More precisely it‘s 9h, 16m and 48s.
      Because 0,28 x 60 is 16,8.
      0,8 minutes are 48 seconds.

    • @walex996
      @walex996 3 ปีที่แล้ว +1

      @@Atook774 Very correct; thanks for pointing it out bro

  • @cyl7014
    @cyl7014 3 ปีที่แล้ว +49

    This riddle is mind-blowing. I figured it out years ago. Nice explanation bro.

  • @bg6b7bft
    @bg6b7bft 3 ปีที่แล้ว

    I got the same answer a different way:
    First, the way they travel is the same as what you suggest.
    Second, I just picked an arbitrary first leg of 1 hour
    T = 1 h, A = 60 km, B = 60 km, C = 15 km
    Third, I calculated where Alex would meet Carl if he backtracked now.
    Carl will cross 1/5 and Bob will cross 4/5 of the 45 km gap between then when they meet. So carl will walk 9 miles, in 0.6 hours, when Bob finds him.
    T = 1.6 h, A = 69 km, B = 24 km, C = 24 km
    Fourth, I calculated where they'd all meet up. Since it's symmetrical, I bet it takes 1 hour.
    T= 2.6 h, A = 84 km, B = 84 km, C = 84 km
    Using this method they travel 84 km in 2.6 hours, which is 32.3 km/h. Their speed won't change when we scale it to 300 km.
    At 32.3 km/h, it takes 9.28 hours to go 300 km.

  • @ryofurukawa1311
    @ryofurukawa1311 3 ปีที่แล้ว +9

    Thanks for sharing the riddle and explaining the results so that we can all understand it clearly.
    I understand these numbers in the question are just out of the blue, but would it be worth mentioning to the interviewers that 15 km/hr is not walking speed. As a running speed, these three brothers are solid ultra marathoners. They ran a little over two marathon's worth of distance under 6 hours.
    After watching many your videos, one thing I learned a lot from you is to really pay attention to every detail and consider every information given. Again, I understand that your videos are meant to share and solve riddles, but it has definitely helped me think outside of the box. Thanks!

    • @LOGICALLYYOURS
      @LOGICALLYYOURS  3 ปีที่แล้ว +1

      Many thanks Ryo for your kind words :) it certainly made me feel confident about my work.

    • @sanskarsinghiit
      @sanskarsinghiit ปีที่แล้ว

      @@LOGICALLYYOURS Hello bro just one question, how much time do you think it will take to solve these type of questions in the interview. I did it in 20-30 mins or so in my home, how long should a person will take it during an interview.

  • @biswarajdutta8494
    @biswarajdutta8494 3 ปีที่แล้ว +7

    This is by far the most impractical thing i have seen in a while

  • @shantanudas6270
    @shantanudas6270 3 ปีที่แล้ว +43

    What an amazing explanation 🔥

  • @hamzavictor2385
    @hamzavictor2385 3 ปีที่แล้ว +4

    So beautifully proven. I did the passive approach and got 11 hours, I was happy thinking I solved it, lol. I love your channel.

    • @ringing7
      @ringing7 3 ปีที่แล้ว +2

      Me too! We missed by several levels of logic 🤪

    • @hamzavictor2385
      @hamzavictor2385 3 ปีที่แล้ว

      @@ringing7 we sure did.

    • @sadikuoluwademilade86
      @sadikuoluwademilade86 2 ปีที่แล้ว +2

      I actually skipped to the end just to realize I was wrong 😂

  • @yogeshbhati1839
    @yogeshbhati1839 3 ปีที่แล้ว +78

    OMG I am feeling sad for Bob that he was being left alone by the biker on a way to his uncle..... Just imagine his feelings 😂😂😂

    • @dorycasalta9432
      @dorycasalta9432 3 ปีที่แล้ว

      lmao 😂

    • @saibhavaniprasad2367
      @saibhavaniprasad2367 3 ปีที่แล้ว +2

      That's the same feeling what Carl was having at the start of their ride.

    • @secretunknown2782
      @secretunknown2782 3 ปีที่แล้ว +2

      No man Bob is the clever he is resting in uncle house and eating all the snacks alone when Alex going back to Carl

    • @yogeshbhati1839
      @yogeshbhati1839 3 ปีที่แล้ว +1

      @@secretunknown2782 lmao but he was walking when Alex and carl riding on their bikes .

    • @secretunknown2782
      @secretunknown2782 3 ปีที่แล้ว

      @@yogeshbhati1839 example 1

  • @vkgamingplatform7247
    @vkgamingplatform7247 3 ปีที่แล้ว

    Khrtnak sandar lajwab mn khus ho gya iska solution dekh ke.

  • @towelie62
    @towelie62 3 ปีที่แล้ว +59

    15km/h that's not walking, that's running, and at a pretty decent pace

    • @theeraphatsunthornwit6266
      @theeraphatsunthornwit6266 3 ปีที่แล้ว +1

      It almost break world record of 21 km hour 😅

    • @МихаилВолков-л2я
      @МихаилВолков-л2я 3 ปีที่แล้ว +1

      Speed of professional race walk athlete on 20 km

    • @mirekkowalski796
      @mirekkowalski796 3 ปีที่แล้ว

      @@МихаилВолков-л2я But here they have to cover almost twice that distance. Absolute world record for 50km walk is 3:32 and its below 15km/h (close to but still below).

  • @ankitlute8160
    @ankitlute8160 3 ปีที่แล้ว +2

    I am not really sure but when I think of the solution, I realise "Alex" was always on the bike during the entire course of the event. Usually (though not always), Optimal solutions are symmetric too. And here, given the fact each of the 3 brothers are identical in every aspect, there seems to be a pressing need of symmetry in the solution.
    That implies, each one of them should get a ride on the bike for the same amount of distance (though in parts) and should get to walk on the road the same amount of distance (though in parts). This in-turn implies, we need to have at least 2 "stops" (or 5, 8, 11, ....) in between so that we can break the course of the event into 3 parts wherein each brother gets to walk for exactly one time (and gets to ride for one time). Makes sense ?
    Great video though @LogicallyYours
    PS: Will take out some time to see if the above actually gives a more optimal solution.

  • @dhairyaprakash7517
    @dhairyaprakash7517 3 ปีที่แล้ว +24

    Answer to this question
    In India :- 5 hrs.
    In abroad :- 9 hrs. 17 mins.

    • @sankarnathan6787
      @sankarnathan6787 3 ปีที่แล้ว

      How is it so?

    • @uddhavsuryawanshi5177
      @uddhavsuryawanshi5177 3 ปีที่แล้ว

      @@navinpnk526 ?

    • @mys-
      @mys- 3 ปีที่แล้ว +3

      @@sankarnathan6787 3 people ride the motorbike at the same time.

    • @devondevon4366
      @devondevon4366 3 ปีที่แล้ว +1

      @@sankarnathan6787 He is going to have the other two (so all three will be on the bike) on the bike (though legally only two persons at most can ride on it), and since 300 km at 60km/hr then it would take him 300/60 =5 hours.

    • @dhairyaprakash7517
      @dhairyaprakash7517 3 ปีที่แล้ว

      @@devondevon4366 You got it 👍🏻✌

  • @NightCrack13
    @NightCrack13 3 ปีที่แล้ว

    Well, my approach was in separation of the whole journey into the three segments:
    1. 1st&2nd pal ride on a bike, while third one walk X time afoot.
    2. 1st pal and 3rd pal walk afoot, while 2nd pal rides back to 3d pal Y time.
    3. 1st pal still walks afoot while 2nd and 3rd ones ride to him on a bike Z time.
    After such division, we'll have the system of three linear equations:
    60*x + 15*y + 15*z = 300
    60*x - 60*y + 60*z = 300 | "-60*y" means that 2nd pal moved backward comparatively to general movement direction
    15*x + 15*y + 60*z = 300
    where, in the end, we got the next values: x = 25/7, z = 25/7, y = 15/7;
    and our lowest time is equal to (x+y+z) = 65/7 -> 9 2/7 hrs.

  • @bapanbiswas4678
    @bapanbiswas4678 3 ปีที่แล้ว +10

    Sir, myself BAPAN BISWAS,19 years old, I paused the video and tried to solve it. It consumed my 45 minutes. But luckily I solved it. I am very happy😇

    • @ravi-k-gupta
      @ravi-k-gupta 3 ปีที่แล้ว

      So basically you'll take 10 hrs 2 mins
      Better anyone take bike, reach your uncle's house, pick him and bring him to your home, it will take 5+5=10hrs...2 min less than your time🤣

    • @bibekaryaal
      @bibekaryaal 3 ปีที่แล้ว

      @@ravi-k-gupta or, even the optimal way would be the uncle starts walking (with the same speed, 15kpm) towards the opposite direction, so that the one with the bike would get him at exact 4 hours and return at exact 4 hours, maybe they could even grab some lunch on their way back and would still reach back quicker🤣

    • @ravi-k-gupta
      @ravi-k-gupta 3 ปีที่แล้ว

      @@bibekaryaal yeah but please consider his uncle is a senior citizen, let's not make him walk and that too at 15kmph😂

    • @bibekaryaal
      @bibekaryaal 3 ปีที่แล้ว

      @@ravi-k-gupta They assume two guys walking 85km constantly with the speed of 15kmph, so why not the uncle walks with the same speed, for a little shorter distance ?🤣

  • @ganesans-mech9572
    @ganesans-mech9572 3 ปีที่แล้ว +14

    If their walking speed is 15km/hr , literally they are sprinting!

  • @mas5621
    @mas5621 3 ปีที่แล้ว +77

    In Asia you will find that upto 4 persons can travel easily on long journey on a BIKE

    • @wpyoga
      @wpyoga 3 ปีที่แล้ว +1

      So true!

    • @blubbubbel4773
      @blubbubbel4773 3 ปีที่แล้ว +1

      I have seen that in the Netherlands too

    • @nijuuu6630
      @nijuuu6630 3 ปีที่แล้ว +3

      Yesterday 4 boys gone on one bike. 16wheel lorry ran over his head . Time is precious but life is priceless.

    • @mas5621
      @mas5621 3 ปีที่แล้ว +1

      @@nijuuu6630 very true that's why I dislike bikes especially in Asia

    • @sudharsananprasath31
      @sudharsananprasath31 3 ปีที่แล้ว +2

      @@nijuuu6630 Thala.... Namma country full ah apdi than iruku...

  • @GDPlainA
    @GDPlainA 3 ปีที่แล้ว

    My working (i have not watched the solution):
    The concept would be 2 people riding while 1 walk. Then, 1 from the bike would walk to the house while the person ride the bike to pick up the person walking from the start. Then they would travel to their destination.
    Setting up variables: We will have the time from the start to where one person would drop off the bike to variable x. Then the remaining time would be variable y. Then, we will create a distance variable named a.
    Working:
    a/15=x (This shows how to calculate x based on a and the walking speed)
    Here, we will start to define variable a
    If that's for walking distance, the bike can travel 4a.
    300-4a would be the remaining distance before the bike travels back.
    The time would be y=(300-4a)/15
    To find the location of where the person walking from the start to the bike would be a+3a/5. The additional distance for the walking person would be 3a/5. The bike distance to meet would be 12a/5. Then to reach the house, they would travel 300-8a/5.
    So another way to calculate y is (12a/5+300-8a/5)/60=y and the simplified one would be (300+4a/5)/60=y.
    Now we could compare (300+4a/5)/60=(300-4a)/15. To balance them, we have 300+4a/5=1200-16a. We can calculate a by using balancing method so it would be 16a+4a/5=1200-300 to 84a/5=900 to a=5/84×900 to a=375/7. Keep it improper fraction for easier use.
    Back to a/15=x, we can make it to x=(375/7)×(1/15). Simplify and you have x as 25/7.
    Back to (300-4a)/15=y, we can make it into (2100/7-1500/7)/15=y. Here, we have y=(600/7)×(1×15). Simplify and you have y as 40/7.
    Now we have values for both x and y, we add them up to find the total time so the result would be 25/7+40/7=65/7.
    Answer: 9+2/7 hours

  • @pramodbadugu9602
    @pramodbadugu9602 3 ปีที่แล้ว +35

    Thing is, if this riddle was there at the time of my Jee advance preparation i surely had done it, now 4 years later my fate brought me here.. Thank you for the explanation

    • @anirvedh
      @anirvedh 3 ปีที่แล้ว

      Bruh your from which IIT ❤️

    • @the_dopeyone6428
      @the_dopeyone6428 3 ปีที่แล้ว +1

      Now are you not in iit??????

    • @TVchristezite
      @TVchristezite 3 ปีที่แล้ว +2

      @@the_dopeyone6428 if he would've, he would've written that he's from 'X' IIT

    • @kryptoknight992
      @kryptoknight992 3 ปีที่แล้ว +3

      How to know if someone is from IIT?
      They'll tell you.

  • @khurram2970
    @khurram2970 ปีที่แล้ว

    Without all these maths, I came up with the answer of a little less than 10 hours. Logic is simple, Alex drops Bob after 4 hours to walk the remaining 60 km on foot for next 4 hours. Then come back to pick the 3rd bro who's resting a bit after walking 90 km in 6 hours. Alex would be back at 90km mark in 2:30 mins and then take him to uncle house 210 km away in 3:hours 30 mins. Bob would have already reached by the time.
    4+2.5+3.5=10 hrs. Less than 10 hours if Carl doesnt wait for Alex after 6 hours and walks a bit further till Alex reaches him.

  • @rownakmondal
    @rownakmondal 3 ปีที่แล้ว +109

    Now, how can one figure this out over there in front of the interviewer?😓

    • @LOGICALLYYOURS
      @LOGICALLYYOURS  3 ปีที่แล้ว +77

      If they give true 10 minutes to think then it's absolutely possible. And I believe all the interviewers must understand this point... that these type of puzzles are not supposed to be answered quickly.... like an instant coffee.... rather they should provide sufficient time to think.

    • @rizka7945
      @rizka7945 3 ปีที่แล้ว +24

      By having the right intuition. I think the explanation on the video was unnecessarily complex. After following this channel for many years and solving similar puzzles elsewhere, the idea of all three brothers arriving at the same time came instantly. Furthermore, it was obvious that there would be at least one drop-off and turning back. Then I realized that with one drop-off there would be two walkers, and in order to arrive at the same time, the walking distances should be equal. Considering the symmetry, the drop-off point should be at 300-x and the pick-up point at x. All this didn't take me more than half a minute.
      The rest is just algebra. On the left side you have the distance travelled by the bike after drop-off. First it drives back 300-2x to pick up the second passenger. Then it has the distance of 300-x to destination. The dropped-off walker has distance of x to destination. From there you have a simple proportion equation. Distance travelled by bike divided by bike's speed is equal to distance travelled by walker divided by walking speed. Getting to this point should satisfy the interviewer.

    • @zombiekiller7101
      @zombiekiller7101 3 ปีที่แล้ว +18

      I did it by another way-
      Let the remaining distance which B has to travel after getting off the bike be x
      Let the distance travelled by the bike after dropping B and picking up C be q
      So 4x=2q+x
      Then q=1.5x
      The other side will be symmetrical so it is also x
      3.5x=300
      Total distance traveled by the bike is 300+2q=300+3x
      =557.142857
      Time=557.142857÷60=9.28 hours

    • @AjayPatel-xr6sz
      @AjayPatel-xr6sz 3 ปีที่แล้ว +8

      @@LOGICALLYYOURS ya may be the interviewer just only want the approach of the candidate to solve this puzzle.

    • @mdabubakar5532
      @mdabubakar5532 3 ปีที่แล้ว +4

      And then there are geniuses like me who proudly calculated 11hrs😂😂

  • @devondevon4366
    @devondevon4366 4 หลายเดือนก่อน

    Let's assume they are traveling 1.4 km instead and divide by the constant
    1.4/1.4 = 1km
    So Alex/Carl will ride to the 1km mark, drop off Carl, and turn around to pick up Bob. Once he picks up Bob, he goes straight to the 1.4 km destination, where Alex/Bob will reach home at the same time as Carl. The
    beauty of the 1.4 constant is that WHEN Alex picks up Bob, they will be at a distance of 4 times away from home as the distance Carl is away from 'home.' And since Alex/Bob is traveling four times the speed of Carl,
    they all will reach at the same time.
    It will take Alex /Carl [ 0.01667 ]hours to reach the 1km
    traveling at 60km per hour.
    Hence, Bob will be at the 0.25km mark since he travels 15 km per hour or 1/4 the bike's speed.
    Alex drops off Carl (recall at the 1km mark) to turn
    around to get Bob.
    Since Alex is at the 1km mark and Bob is at the 0.25 km
    mark, they are 0.75 km apart . So, how long before
    they meet? It will take them the 0.75km divided by
    75 km per hour or 0.01 hours
    So, at what distance will Bob travel in [0.01] hour?
    Distance = speed * time = 15km per hour * 0.01
    = 0.15km
    But since he has already traveled 0.25km, when Alex
    meets him, he will be at the 0.40 km mark (0.25 + 0.15)
    So where is Carl? Since he walks at the same speed
    as Bob, he travels for 0.15km. So, now Carl is
    at the 1.15km mark (1 km + 0.15km)
    Notice that Carl is now just 0.25km away from home (
    1.4 km - 1.15 km = 0.25km),
    and notice that Alex/Bob is 1km from home (1.4 km - 0.40km).
    Notice that 1km is 4 times the distance of 0. 25 km,
    Hence, since Alex/Bob is traveling four times, Carl,
    all three will reach 'home' at the same time.
    So, how long before they reach home?
    1km divided by 60 miles per hour
    or 0.25km divided by 15 miles per hour. Either one will
    give you the exact time 1/60 = [0.01667hour]
    So let's add up all the hours travel so far
    0.01667
    0.01
    0.01667
    -------------
    0.04334 Total hours to reach 1.4 km
    It takes 0.04334 hours to reach 1.4 km (say they do this every week)
    But the total distance is not 1.4 km, it is 300 km
    So, let's divide 300km by 1.4 = 214. 2857
    Then let's multiply this by 0.04334
    Hence, 0.04334 hours * 214.2857 =9.287 hours
    Answer

  • @manurohit6867
    @manurohit6867 3 ปีที่แล้ว +15

    Alex so lucky just drop and receive Bob and Carl😂😂😂

  • @aravindboniy-t5505
    @aravindboniy-t5505 3 ปีที่แล้ว +5

    Lol better take the uncle to there (Three brothers home)😂😂

  • @NikhilSingh-gb1eb
    @NikhilSingh-gb1eb 3 ปีที่แล้ว +27

    They stopped at a restaurant and took rest for 5 hours
    Wasted their money and come back to their home
    🤣🤣

    • @mirekkowalski796
      @mirekkowalski796 3 ปีที่แล้ว +1

      Meanwhile Carl was walking on expecting to see Alex on bike pretty soon 🤣😂.

  • @wompastompa3692
    @wompastompa3692 3 ปีที่แล้ว +6

    >walking at 15km/h
    Damn, those brothers are pretty fast.

    • @HumbugShow
      @HumbugShow 3 ปีที่แล้ว

      That was what I thought. The correct solution is that you can't walk at 15km/h therefore the person who wrote the question should be fired and the QC of the questions as well. I just saved Google about $300k p.a

    • @MotorBorg
      @MotorBorg 3 ปีที่แล้ว

      Probably was written by an American who had no idea what the hell a kilometer is. :)

  • @migueldelmazo5244
    @migueldelmazo5244 3 ปีที่แล้ว +4

    Wonderful video, and the logic is beautifully explained.
    However, for countries where this scenario is a common occurrence, I propose another solution. The third person hangs precariously from the motorcycle, and all three riders hang on and pray for 5 hours until they get to the uncle's house.
    I would also predict that the driver would never let off the motorcycle's horn the entire trip. :)
    Your videos are always awesome. Thanks again.

  • @Marque734
    @Marque734 3 ปีที่แล้ว +1

    I found this much easier:
    Brother 1 and 2 drive 1 h: 60km
    Brother 3 walks: 15 km
    Brother 2 drives back: meets Brother 3 after 36m - brother 1 walked 9 further kilometer
    There is a gap between the brothers of 45 km now.
    At a catch up speed of 45km/h it takes them another hour to all meet again.
    All brothers are together with their bikes at Kilometer 84 after 2,6h. They moved with 32,3 Km/h with that speed it takes them 9h 17 minutes and about 48 seconds to reach the goal.

  • @TREMILBERG
    @TREMILBERG 3 ปีที่แล้ว +14

    I would love to see anyone "walking" 85km at 15km/h.

  • @devondevon4366
    @devondevon4366 3 ปีที่แล้ว

    Bob could ride Alex to the 214.285 km Mark. This would take 3.5714 hours (214.285/60) while Carl would be at the 53.57 km mark (214.285/4) since he is walking 1/4 the bike's speed (15/60). The distance between Bob/Alex and Carl is now 160.713 km. Bob drops off Alex to return for Carl, and it would take Bob 2.1428 hours (160.713/75) to reach Carl. Carl then would walk just 32.142 km (2.1428 x 15) while Bob would ride for 128.57 km (2.1428 x 60 or 32.142 x 4) before they met. Bob and Carl are now at the 85.714 km mark (214.285- 128.57 or 32.142 + 53.57), while Alex is at the 246.427 km mark (214.285 + 32.142), AND they have so far completed 5.7142 hours (3.5714 + 2.1428).
    Bob and Carl now have 214.285 km to reach the destination, while Alex has 53.57 km to reach the destination. But since Bob and Carl are traveling at 4 times the speed Alex is walking, and since 214.285 is four times 53.57, they would reach the same time or in 3.5714 hours ( 214.285/60 or 53.47/15). Total hours to reach hence = 5.7142 + 3.5714 or 9.28 hours or 9 hours and 17 minutes (Answer) (8:13) (8:26)
    PS
    So Bob rode 557.14 km in total (214.285 + 128.57 + 214.285), 257.14 km MORE THAN the 300 km journey,
    while Carl and Alex walked 85.714 km and rode with Bob for 214.285 km (notice that 85.714 + 214.285 =300km). Since all three reached the same time, by just dividing Bob's 557.14 km on the bike by 60 miles per hour, you still get 9.285 hours (the Answer). And if you divide Carl's (or Alex's) 85.714 km walking by 15, you get 5.714 hours, then divide their 214.285 km (riding with Bob) by 60, you get 3.5714. And 5.174 + 3.5715 also = 9.28 hours.
    The 214.285 km (the drop-off) came from dividing 300 by 1.4 from a formula I created.
    PS
    The key is once all three started the journey (riding and walking), no one stops (except when Bob drops off Alex to return for Carl to pick him up, yet Alex has to begin to walk immediately, and Carl also has to continue to walk towards Bob, though Bob is riding to get him), and they must reach their uncle's house EXACTLY the same time. What if Bob drops off Alex at the 250 km mark (as opposed to the 214.285 km mark)? Then Alex would reach first (before 9.28 hours), but the time would be greater than 9.28 hours or 9 hours 17 minutes for all three, which they don't want.
    PS.
    The difference between Alex and Clark during the 300-km journey was that while Alex walked 85.714 km at the start of the trip and rode 214.285 at the end of the trip, Clark walked the same distance but at the end of the trip and rode the same distance but at the start of the trip (214.285 + 85.714 = 300km).

  • @kuga5197
    @kuga5197 3 ปีที่แล้ว +10

    I haven't commented on this channels after videos for many times ,because those last videos are simple ,but not gonna lie this one is pretty unique. Keep loving your videos

  • @kasperkerkhof2252
    @kasperkerkhof2252 3 ปีที่แล้ว +1

    I solved it using a shorter solution. I divided all parameters by 15 (total distance 20km, walking 1km/h and bike 4 km/h). I knew by logic Bob and Carl would run an equal distance X, and time for Carl(=Bob)=Alex resulting in:
    X/1+(20-X)/4 = 2*(20-X)/4+(20-2X)/4
    Eliminate ():
    X+5-X/4 = 10-X/2+5-X/2
    Solve for X:
    X=40/7=5.71
    Fill X in original equation:
    5.71/1+(20-5.71)/4=9.28h
    Much easier 😉

  • @samirshah6610
    @samirshah6610 3 ปีที่แล้ว +4

    Loved this puzzle, made you think harder. Thanks

  • @arjunsharma5078
    @arjunsharma5078 3 ปีที่แล้ว +4

    Carl and Bob be like : hatja aaj bike tera bhai chalayega 😂😂😂

  • @dishu__gamerz7185
    @dishu__gamerz7185 3 ปีที่แล้ว +4

    Amazing puzzle and the way of solving is also awesome.

  • @lakshyakumar4459
    @lakshyakumar4459 3 ปีที่แล้ว +3

    Logic dictates they found a solution but are looking for way to make it shorter therefore never reaching their uncle's house

  • @thomasfriis3651
    @thomasfriis3651 3 ปีที่แล้ว +7

    I’m just impressed that they walked 15 km/h

  • @entity3675
    @entity3675 ปีที่แล้ว

    I calculated it a bit differently.
    a = walking speed = 15
    b = bike speed = 60
    h1 = the time it took for Bob to get to x on bike
    h2 = the time it took for Alex to get to z after dropping Bob off at x on bike OR the time it took Carl to get to z by walking
    h3 = the time it took for Alex and Carl to get to their uncle's house on bike from z OR the time it took for Bob to get to his uncle's house by walking after h2
    We can describe the brothers' journey like this
    Bob: h1b + a(h2+h3) = 300
    Alex: b(h1-h2+h3) = 300
    Carl: a(h1+h2) + h3b = 300
    (Bob & Carl)
    h1b + h2a + h3a = h1a + h2a + h3b
    h1b + h3a = h1a + h3b
    h1b - h3b = h1a - h3a
    b(h1 - h3) = a(h1 - h3)
    Canceling out the h terms would entail that a and b are equal, but this is not true. This implies that we're somewhere dividing by zero. Therefore the only way for this equality to make sense is for (h1-h3) to be 0, that is: h1=h3
    (Alex & Bob)
    b(h1-h2+h3) = h1b + a(h2+h3)
    b(2(h1) - h2) = h1b + h2a + h1a
    b(2(h1) - h2) - h1b = a(h2+h1)
    b(2(h1) - h2 - h1) = a(h2+h1)
    b(h1-h2) = a(h2+h1)
    b = 4a -> 4a(h1-h2) = a(h2+h1)
    4h1 - 4h2 = h2 + h1
    3h1 = 5h2
    h2 = (3/5)h1
    Now we can solve the puzzle.
    h1 + h2 + h3 = (13/5)h1 = ?
    (Bob)
    h1b + a(h2+h3) = 300
    h1(4a) + h2a + h3a = 300
    a(4h1 + h2 + h3) = 300
    (15)(4h1 + h2 + h3) = 300
    4h1 + h2 + h3 = 20
    4h1 + (3/5)h1 + h1 = 20
    (28/5)h1 = 20
    13/28( (28/5)h1 = 20 )
    (13/5)h1 = 9.28...

  • @mr.yamonga
    @mr.yamonga 3 ปีที่แล้ว +9

    Wait! Uncle is wasting time call the uncle and fix a piont in the middle of root save time😀

  • @manillheirent8530
    @manillheirent8530 3 ปีที่แล้ว +1

    Took me exactly 13 minutes to figure it out. Very good riddle!

  • @justingolden21
    @justingolden21 3 ปีที่แล้ว +6

    Bob's legs after doing 86km at 15km/h (53mi at 9mph) 💪🦵

    • @mirekkowalski796
      @mirekkowalski796 3 ปีที่แล้ว

      Bob looks pretty young and healthy. Think about Carl!

  • @Eiger2112
    @Eiger2112 3 ปีที่แล้ว

    So Alex starts walking, while Bob drives the bike with Carl on the back, and drops him off before the house at point C. Bob then returns to pick up Alex who has been walking all that time. They then drive to the house and arrive right as Carl is walking up.
    I used simultaneous equations.
    So there are 2 key points:
    A = The point that Alex reaches walking before he is picked up by Bob
    C = The point that Carl is dropped off to finish walking to his uncle's house
    Equation 1:
    So the TIME it takes Alex to walk to point A must equal the time it takes Bob (always on the bike) to drive to point C (drop off Carl) and then return to A:
    A/15 = C/60 + (C - A)/60
    4A = C + C - A
    5A = 2C
    A = (2/5)C
    Equation 2:
    The time it takes Carl to walk the remainder of the way to the destination must equal the time it takes Bob to return from point C back to A, pick up Alex, and then drive to the house:
    (300 - C)/15 = (C - A)/60 + (300 - A)/60
    4(300 - C) = C - A + 300 - A
    1200 - 4C = C + 300 - 2A
    5C - 2A = 900
    Substitute result from Equation 1:
    5C - 2(2/5C) = 900
    5C - (4/5)C = 900
    4.2C = 900
    C = 214.3
    then:
    A= (2/5) 214.3 = 85.7
    So (Alex walks 80 km) while ( Bob drives 200 and drops Carl off and then returns ). Total Time can then be calculated to be time it takes Alex to walk 80 km and then drive (with Bob) the remaining 220 km:
    Time = 85.7/15 + 214.3/60 = 5.7 + 3.6 Hours = 9.3 hours

  • @muhanishchouhan9501
    @muhanishchouhan9501 3 ปีที่แล้ว +17

    How bob will feel when you drop him 50km before destination

  • @Jadinandrews
    @Jadinandrews 3 ปีที่แล้ว +1

    Uber driver: ok you walk from here
    Me: why?
    Uber driver: I don't have time to explain

  • @arquamkhan2362
    @arquamkhan2362 3 ปีที่แล้ว +8

    When I did by my own I got 11 hours...🤪
    But now I know the correct approach 😃
    Thank you AMAR sir💖😊💖

  • @Nil-js4bf
    @Nil-js4bf 8 หลายเดือนก่อน

    Got the answer on the first try by solving for x where 300-x was the first drop off point. Algebra was simple but was a pain to sub x back into the equations for t1 + t2 + t3.
    t1 = (300-x)/60
    x1 = t1 * 15 = (300-x)/4
    x2 will be the point where the walker and the bike meet up and since the bike is 4 times faster than the walker, they meet at 1/5 the distance between their initial positions. So
    x2 = x1 + 1/5 * [(300-x) - x1] = x1 + (3/20)(300-x)
    t2 = (3/20)(300-x)/15
    t3 = (300 - x2)/60
    Since everyone arrives at same time, 15(t2 + t3) = x
    Substitute t2 and t3 into that and x = 1800/21
    Then substitute x to find the total time = t1 + t2 + t3

  • @josephkong44
    @josephkong44 3 ปีที่แล้ว +5

    I don't think this question is hard enough to be an interview question of google. I solved this in 2 minutes and the solution is much cleaner.

    • @itsomi2167
      @itsomi2167 3 ปีที่แล้ว +1

      Best solution is to use public transport

  • @satyamsagarsatyarthi9561
    @satyamsagarsatyarthi9561 3 ปีที่แล้ว +1

    I solved it after seeing thumbnail and i found answer which was 11 hrs.
    But to know was i correct so i started to watch this video and i memorized book of OPTIMAL SOLUTION in my B.Tech. and again i found the answer which was 9.28 hrs.👍 Woww nice video THANKS.

  • @alanbrogan2642
    @alanbrogan2642 3 ปีที่แล้ว +5

    lemme tell you , " They don't ask these type of questions.These are easy . They usually tell you to solve complex math problems with your preferred programming language. Stay in school , don't trust this."

    • @indianbot0077
      @indianbot0077 3 ปีที่แล้ว

      How do you know? Utube is full of these kind of videos ,famous math utuber 3blue1brown also upload these kind of problems.

  • @riemerbeets997
    @riemerbeets997 2 ปีที่แล้ว

    My solution: after one hour person 1 and 2 (on the bike) have travelled 60 km, person 3 has walked 15 km. The difference is 45 km. If person 1 drops off person 2 so person 2 can walk further and person 1 drives back to pick up person 3, they have to travel 45 km to reach eachother. Because they go in opposite directions their cumulative speed is 75km (45km / 75 km = 0,6 ) This means that in 1,6 hours person 1 and 3 meet eachother at 24 km from the starting point. Person 1 has also travelled 9 more kms (69km). After one more hour, at 2,6 hours all three persons would meet up at 84 km from the starting point. Since they all traveled the same distance (84km) in exactly the same amount of time (2,6 hours) - which is basically what this question asks, I just simply divided the 300km by the 84 km I calculated and multiplied that by the time required to travel that distance (2,6 hours) = 9,285714.

  • @ajeeshjb1143
    @ajeeshjb1143 3 ปีที่แล้ว +6

    I got an answer 65/7 without this much complex, but I don't know my method was right!

    • @sravanyadhav3977
      @sravanyadhav3977 3 ปีที่แล้ว

      Ya bro near 9.2 hrs

    • @indianbot0077
      @indianbot0077 3 ปีที่แล้ว

      Did u solved using three variables and considering the as the three time intervals??? Plz tell.

    • @Antonio_Serdar
      @Antonio_Serdar 3 ปีที่แล้ว

      @@indianbot0077
      Two time intervals, the first one is until the motorcycle turns, and the second one is the time to pick up the last brother + drive to the finish line.

  • @PMcMonty
    @PMcMonty 3 ปีที่แล้ว +1

    This answer in this video is so convoluted... Here is how I solved it: The biker goes away from the walker at 45 and towards at 75... so to swing around and pick up the slower walker, it takes 45/75 = 0.6 times as long as the biker spent going forwards. Once the bike picks up the walker, its just gonna go forwards again for the same time as it did when it had the carried the first passenger, so thats a total of 2.6 time units forwards, of which it spent 0.6 going backwards(which counts as negative), so its as if it only went forwards by 1.4 out of the full 2.6. Traveling at regular speed, the bike takes 5 hours, so 5 * 2.6/1.4 = 9.285.

  • @adityakumarsingh6402
    @adityakumarsingh6402 3 ปีที่แล้ว +4

    One of the genuine puzzle channel. Keep it up✌️✌️

  • @Herr_Vorragender
    @Herr_Vorragender 3 ปีที่แล้ว +2

    If I were Bob, I'd be mad at Alex for dropping me off half way and making me walk 85+ km

  • @joshparker5779
    @joshparker5779 3 ปีที่แล้ว +16

    I literally spent almost an hour thinking this through. It's been way too long since I quit studying math ... :( I'm just relieved that I got the right answer :)

    • @grasgruen84
      @grasgruen84 3 ปีที่แล้ว

      haha it took me only 3min to get the wrong answer, because as a practical person 2 dudes went to final destination with the bike and then he turned to get his mate :P thats how we did it when we were young and didnt have a car, that makes the equation way easier :P hey it only took them 11h :P

    • @DiogenesNephew
      @DiogenesNephew 2 ปีที่แล้ว

      @@grasgruen84 Same lol

    • @akmusic2037
      @akmusic2037 ปีที่แล้ว

      ​@@grasgruen84Relative motion😅

  • @svarodzic
    @svarodzic 3 ปีที่แล้ว

    Wow! Can't believe Google still does that!? The only thing you can find out by interviewing engineers like this is a guy who can solve riddles very well. But it has no correlation with how good a person can actually write code!

  • @mohsinraza7348
    @mohsinraza7348 3 ปีที่แล้ว +4

    What If the Uncle also start walking at the same time from opposite direction

    • @pharkasj
      @pharkasj 3 ปีที่แล้ว

      with his house in the backpacket.

  • @william7yifans
    @william7yifans 3 ปีที่แล้ว

    My approach:
    I tried to find the overall optimal speed (km/hr) they can achieve as a group of 3, by using an example of a + b on the motorcycle for an hour, then a meets with c 0.6 hours after when backtracking to pick him up, and then them meeting up again at 2.6 hours at a distance of 84km from home. this gives us a net optimal speed of 84km/2.6hr, or (84/2.6)km/hr, so the time it takes to travel 300 km would be 300*2.6/84 hours, or if you must simplify, 75*2.6/21 hours, returning 9.28571

  • @CultOfJ
    @CultOfJ 3 ปีที่แล้ว +4

    Absolutely brilliant ❤️❤️

  • @koyavasudhalakshmi2073
    @koyavasudhalakshmi2073 3 ปีที่แล้ว +1

    Very nice explanation sir 🤩🤩

  • @maruthasalamoorthiviswanat153
    @maruthasalamoorthiviswanat153 3 ปีที่แล้ว +10

    It's really interesting and tough one for me.

  • @gandhimathim8784
    @gandhimathim8784 ปีที่แล้ว +1

    My Solution :-
    2x+y = 300 .... (1)
    Time taken by the driver to reach the destination :
    t = (2x+3y) /60 ... (2)
    Time taken by the other guys to reach the destination :
    t = (5x+y) /60 ... (3)
    From (2) & (3)
    y=3x/2
    Substitute y in (1)
    x=600/7
    y=900/7
    Substitute x&y values in either (2) or (3)
    t=65/7 = 9.28 hr

  • @mathsman5219
    @mathsman5219 3 ปีที่แล้ว +7

    The exact answer is 9hours,17 minutes, and 60/7 seconds

  • @danyalshamsi1161
    @danyalshamsi1161 3 ปีที่แล้ว +4

    Thanks a lot, sir. Solving this puzzle lifted my spirits up. Keep posting regularly.

  • @brazen_helm
    @brazen_helm 3 ปีที่แล้ว

    This is the way I thought about the problem:
    First of all, it is clear that in an optimised solution at all times either two brothers will ride the bike forwards and the other one will walk forwards, or one brother will ride the bike backwards and the other two will walk forwards. Let's call these methods of travel method 1 and method 2.
    In method 1, the total position of the brothers is moving forwards at 135km/h (60+60+15) while in method 2 it is moving backwards at 30km/h (15+15-60). Meanwhile in method one the position of the bike is moving forwards at 60km/h while in method 2 it is moving backwards at 60km/h.
    Over the entire journey, the total position of the brothers moves forwards by 900km (300km * 3) and the position of the bike moves forwards by 300km.
    Let X be the amount of time spent travelling using method 1 and Y be the amount of time spent travelling using method 2. Putting this together we get the following simultaneous equations:
    135X - 30Y = 900
    60X - 60Y = 300
    We are interested in X + Y. These equations can easily be solved to give X + Y = 65/7 hours, or approximately 9 hours 17 minutes.

  • @rahilhabib
    @rahilhabib 3 ปีที่แล้ว +6

    Alex forgot about the new road works which meant he had to divert his route half way and add an extra 300km to the distance. Bob still ends up wasting time. Carl is very tired as a result and doesn't enjoy the visit to their uncle's house.

  • @200644600
    @200644600 8 หลายเดือนก่อน

    I calculated the same results before watching the video. The question is classic travelling time problem and it should be completed without much effort. The use of (distance of the point of return for the bike) and the (distance of the point of pickup) are enough to solve the two variables in two equations.

  • @karl-heinzfurtz8210
    @karl-heinzfurtz8210 3 ปีที่แล้ว +3

    I would need the acceleration and the breaking time of the bike 🤓🥸🤷‍♂️

    • @I_am_Itay
      @I_am_Itay 3 ปีที่แล้ว

      Lol nice, infinite power here I come

  • @vietlongpro
    @vietlongpro 3 ปีที่แล้ว

    1. Human being:
    Who can walk 15km/h in 5 hours continuously, the Olympic champions! But, all of them only have 1 motorbike, it's okay, they'll ride all three. Riding motorbike at 60km/h for 5 hours is crazy, they drive 100km/h minimum.
    Answer: 3h30m (30 minutes to urinate and take a break in the middle of the road).
    2. Machine:
    - 5 hours: first 2 people arrive at uncle's house 300/60 = 5
    - 3 hours: return to pick up the next person (300 - 5*15) / (15 + 60) = 3
    - 3 hours to go back uncle's house
    Answer: 11h for all to arrive.

  • @amiruddinsyah3505
    @amiruddinsyah3505 3 ปีที่แล้ว +9

    It doesnt matter if they have a car. Problem solved. And everyone is happy.

  • @yashwanthcv8315
    @yashwanthcv8315 3 ปีที่แล้ว

    Alternate solution
    We know optimal solution involves a drop off and a pick up. Let X be distance b/w start and pick up point, Y be distance between pick up and drop off point and Z be the distance between drop off and end.
    X + Y + Z = 300 --------------> Let it be 1
    They can save time only if all of them reach their uncle house together, therefore time taken by each person to reach their uncle's home is same let it be T
    T = ( X+Y / 60 ) + (Z /15) ---------------> Let it be 2 {person who walked in the last}
    T = ( X / 15) + ( Y+Z / 60) ----------------> Let it be 3 {person who walked in the beginning}
    T = ( X+Y / 60) + (Y / 60) + ( Y+Z / 60) --------------> Let it be 4 {person who was on the bike all the time ....clever guy😂}
    Now equating 2 & 3 gives X = Z and equating 3 & 4 gives Y = 1.5X
    Solve X=Z Y=1.5X X+Y+Z=300 to get X, Y, Z as 85.7 , 128.6 , 85.7 respectively
    Substitute these values in any of the equation 2, 3 & 4 to get min time taken to reach home.
    For example
    T = ( X+Y / 60 ) + (Z /15) T = ( 85.7+128.6 / 60 ) + (85.7 /15)
    T = ( 214.3 / 60 ) + (85.7 /15) T = (3.5716) + (5.7133)
    T = 9.284933 hr
    🔥🔥🔥🔥🔥
    ☮️ ☮️ ☮️ 🧪 🔥
    ☮️ ☮️ ☮️🧪 🔥🔥🔥🔥🔥
    ☮️ ☮️ ☮️🪥🪥🪥 🔥
    ☮️☮️☮️ ☮️ ☮️ ☮️ 🪥 🔥🔥🔥🔥🔥

  • @s18gyan84
    @s18gyan84 3 ปีที่แล้ว +9

    "A" person is also wasting her time by giving lift to B and C