Most US College Students Get This Wrong
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- เผยแพร่เมื่อ 27 มิ.ย. 2024
- To complete a job, it takes: Alice and Bob 2 hours, Alice and Charlie 3 hours, and Bob and Charlie 4 hours. How long will the job take if all 3 work together? Many, many US college students set up the equations incorrectly and get the wrong answer. Can you solve it? Watch the video to understand the correct method and answer.
*Small correction: At 2:19 I incorrectly said "four fifths" and meant to say "four point five."
0:00 Problem
1:00 Common mistake
3:14 Solution
My blog post for this video
wp.me/p6aMk-5h1
Sources
Toom, Andrei. "A Russian teacher in America." Journal of Mathematical Behavior 12.2 (1993): 117-139. See the "Tom, Dick, and Harry working together problem" (page 134 in text). faculty.utrgv.edu/eleftherios...
Jerome Dancis, Associate Professor Emeritus, University of Maryland, Algebraic word problems. www.math.umd.edu/~jnd/Algebraic_word_problems.pdf
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4.5 is now pronounced "four fifths" (2:19).
..so .11 is pronounced "zero elevenths"?
Rofl, gold. The true riddle is solved.
CQUNC I noticed that too. xD
9/2 = 4/5 good to know
#FakeMath
I work in software development, and everyone in that field knows that the more programmers you assign to a task, the longer it will take.
was looking for this comment
You don't even need to be a software developer to understand. Chefs working with limited kitchen space is a good enough example of this. The most important thing is that there needs to be an adequate amount of work for each person to work efficiently. Software development has plenty logistical implications that come from bigger teams.
First Surname its a joke
Funnily (or not) enough, it's based (and reinforces) a belief that can have a negative impact on planning...
+Nathan How so? I think people understand when a larger team is needed for a task, and when a task can be done by a smaller team. It's mainly just common sense. Having too many people on a simple task just wastes man hours (which are expensive). Conversely, having too few people on a big task however risks you not meeting deadlines.
Again to use food as an example. A waiter knows what it's like to both be over-staffed and under-staffed.
This saying is not a religious belief. The saying arose because of observations.
Answer is 0. They’ve already done the job 3 times.
Obviously they all did it wrong if they have to do it again. I wouldn't trust them to get it done in their combined times let alone 1hr51min.
It's shoveling snow
Lol
Lol
SupremeHorizon not necessarily. They could be vaccuming the house and they do it each week.
i'm more astonished by the fact that charlie makes the job only NINE MINUTES shorter, than by the actual solution itself
In 1 hour he does 1/7th as much work as Alice.
Charlie must be part of management.
ikr 😂
I took a detour and I think I found out it takes Charlie 24 hours to complete the task on his own. I think it takes Alice 3.42 hours on her own.
@@TheLastSoundNL Even Bob by comparison does the job in 4 hours and 40 minutes just by himself.
Also, Alice takes about 3h26 to do a solo job, Bob takes 4h48, and Charlie takes a whopping 24h.
The conclusion : fire Charlie and hire someone else.
u calculated for each person?
The conclusion: Charlie is the manager and Alice is working a summer job until she finishes college. Bob is Bob.
@@BigMac4459 Bob is Bob
I'm surprised that Bob would agree to work with Charlie again, seeing as he has to spend twice as long at work if he is paired with Charlie, compared with when he is paired with Alice.
@@kwilson5832no choice- charlie makes the schedules
I know this is a math problem and all, but everything I've seen in many different jobs tells me that Bob and Charlie should get out of the way so Alice can fix everything, so they can all go home.
LOL
So true...
Charlie discarded only 9 minutes of Alice's and bobs work, what a useless person
Bob and Charlie are distracted by Alice's feminine attributes! 😜
Especially Charlie. Poor sod can't think straight it seems...
Definitely
The real answer is: "Charlie you only saved us 9 minutes. You're fired.”
316ht under rated comment
Agreed
it took bob and charlie 4 hours to do the job that alice and bob did in 2. charlie needs to get fired
Exactly. Well put 316ht.
Hahaha this is gold
I thought about it a little differently than the 'percentage' system. I thought of them as rates. Alice works at 'a' jobs per hour, Bob at 'b' jobs per hour, Charlie at 'c' jobs per hour. Adding their rates together, Alice and Bob would work at the rate of 1 job per 2 hours, so the equation is A + B = 1/2, with the units being 1 job / 2 hours. So you'd get:
A + B = 1/2
A + C = 1/3
B + C = 1/4
Using the neat little trick and adding all of them together, you get
2A + 2B + 2C = 1/2 + 1/3 + 1/4
2(A + B + C) = 6/12 + 4/12 + 3/12
A + B + C = 13/24
All of them together can work at the rate of 13 jobs per 24 hours, and if you want to know how long it takes them to complete 1 job, just invert the answer: 24/13 ≈ 1.85 hrs. Charlie needs to step his game up.
This is the way I did it. You quickly see that you have to deal with rates due to all working simultaneously. The wrong answer of 4.5 is actually correct if A, B, and C have to work sequentially and not in parallel.
I used this method too! And it's crazy how many people got it wrong, since I was taught this in 8th grade
That's how I solved it too, in my head in 15 seconds. 😊
That’s basically how I figured it out, too
@@micknamens8659took me longer than 15 seconds, lol
as someone who worked in groups, i can safely say that more people does not always equal less time, sometimes it's much faster to do something alone or with 1 person than with 3 or 4 or 8 or whatever, things often get wrong when there's too many people
Which is why there was a condition given at the beginning saying that their work rate is constant no matter whether they work together or separately. As an example, there are three production lines on which boxes are being closed by the workers. The boxes come from a single source and go to whoever pushes a button by their position. The amount of work any of them do have no effect on anything the rest does, meaning that there's nothing either can do to affect the work time the others do, except by shortening it (since the amount of boxes to close will be lowered by whatever that person manages to do).
That being said, lowering the time by 9 minutes? So...Charlie is so lazy that he basically does nothing?
@@kikixchannel I’d personally go with “that isn’t in the spirit of the question” but if we are talking about technicalities, the question doesn’t state that the job benefits from multiple people working on it. For example, baking has a step that says “pop it into the oven and wait for an hour”. All 3 of them constantly wait at a speed of 1 minute per minute, none of them spend a longer or shorter amount of time waiting. However that doesn’t mean that the cake would bake any faster even if all 3 waited for it together.
@@zikli9249 That view however goes cross to the data in which everyone has a different work time, so there are actions actually being done. There is no fixed delay time.
@@kikixchannel Not necessarily, since the data only mentions the time it takes for each pair to complete the job. If the job was "bake a cake" it has a built in delay time since the job (and the cake) is not finished until the cake itself is fully baked. Generally, Alice and Bob spend 2 hours to bake a cake doesn't imply that they spent 2 hours mixing ingredients, but rather the full time to come out with a finished product.
However, even assuming that there is no fixed delay time. Let's take another example -- there are 3 cities in a straight line: A, B and C. Each of the cities is 1 mile apart. The job is to deliver a package from City B to City A and a second package from City B to City C. Assuming Alice and Bob both walk at 1 mph, Alice alone would take 3 hours to finish the job (pick both packages up from B, take an hour to move to City A to drop off a package, take 2 hours to move to City C to drop off a package). Bob would take the same amount of time. Working together however, Alice and Bob can complete the task in 1 hour, where they each take a package and deliver it to a different city. Them working together on this allowed them to completely skip a part of the journey.
Either way, all of this is ignoring the spirit of the question.
Yeah. It takes nine month for woman to born a child, how much time it takes for nine women?
"When 3 people work together they should take less time than 2 people."
I feel charmed by your naivity.
Three people is a Union, and the job never gets done.
The work effort each put out is a constant
Paul Googol the key word is should
@@hermanstanford4388 a constant struggle
@@hermanstanford4388 You can work at a constant rate and still end up worse off than when you started.
The answer is that Charlie will be unemployed VERY soon.
Naihonn. Agreed... So the answer will become 2 hours. 😎
Naihonn I think Charlie must have shown up to work in a full body cast.
Naihonn I have lived a few years and my experience is the less capable you are. The better job you get. Stop trying so hard. Life is easier than you think.
What a life moto. Stick to being incapable kids!
Charlie works at a Union wage and at a Union pace.
I approached the equation almost the same, but keeping fractions on the right instead of factors at the left.
I think the formula becomes easier to think of once you rephrase "Alice and Bob completed a job in two hours" to "Alice and Bob complete one job per two hours", leading to an elegant A+B=J/2h.
After that it's just adding the fractions to get
2(A+B+C)=13J/12h
A+B+C=13J/24h
Then reason out that if they can do 13 jobs per 24 hours, they can do 1 job per 24/13 hours.
That's what he left out of his solution, and why it looks like he made a crazy leap to get the right answer.
This was amazing👍
My method.
This is how I solved it. It makes it feel much more like physics, and more intuitive to me than whatever was done in the video.
Same here. "A and B takes 2 hours to do the job". So i made (A + B) * 2 = X. And so on and so far.
When I saw this problem I instantly thought about adding resistors in parallel and got the right answer 😊
That fact that work is a rate of units/time and resistance is "a rate" V/I means this analogy works perfectly !!
Brilliant !
bro same here, i just love physics so at seeing the hours i just assumed humans to be resistors and put up the parallel combination equations and the answer just came to me. i have never felt more proud
Yesss that’s exactly what I did!!!
ayo bro if u don''t mind can u elaborate your explanation? i'm quite weak in maths and science
ayo damn i ever thought like this damn thats a great analogy im just amazed.. Good thinking !!
“More people working on a project should get it done quicker.”
Oh, honey.
Depends how many of those are managers
FOR REAL
Charlie seems like dead weight, he just sits back while Alice and Bob do it in 2. solved easy
Problem kind of ignores diminishing returns. Picture three people working in a 5X8 foot bathroom, one painting, another installing a new supply and faucet to the sink, and the third putting in a shower surround. Total job will get done faster if they work on their individual part at different times.
Also, yeah, Charlie should be fired, and from the look of the times Alice might deserve a raise.
That was my thought too, realistically it probably took the 2.5 hours with all of them working on it.
"When 3 people work together, it should take less time than when only two people work together." You've clearly never worked with a "Charlie" 🤦♂️
Group projects always take longer. Murphy's Law demands it.
Yup - in my experience if you have 2 people wo are really good at their job (like Bob and Alice clearly are) and you add a third worker who is a dog... the first answer is probably more accurate.
"Too many cooks spoil the broth." Its a proverb for a reason.
Haha sooo true!!!
@@Fickji nope.
I have 20 years working as an engineer. After i solve any problem, I always apply a common sense check. This is something i see most beginning engineers skip and it causes them to not catch most of their errors until the errors have culminated into an obvious failure.
As a side result, we can notice that Alice's relative working efficiency is 7, Bob's 5 and Charlie's 1.
Yep!
my brain immediately went “well alice and bob are still part of the group so it’s still 2 hours because they would just ignore charlie since he’d be slowing them down”
Judging just by what the problem reads, Bob is either the slowest worker or he tells a lot of really good jokes.
That was my conclusion as well
I concur dr
You’re right because it takes 9 minutes faster with Charlie because he helps for the first 5 minutes then sits in the corner.
That was my thought too. I thought it was a trick question like "if a rooster lays an egg on a roof, which direction does it roll?".
"It takes less time than any pair working together."
Sounds like you have never been involved in a group project in college.
Do they work at a constant rate?
@@carrymesenpai3276 no
@@jacobmontemayor6685 obviously, which makes this comment kind of obsolete, an out of context joke at best
In college? in the real world.....the more people involved, generally, the longer it takes.
@@muskokamike127 yes but that was never subject of the discussion
I arrived at the correct answer in what was to me a much simpler way. I said to myself that they are cleaning cars and I noticed the usefulness of 12 as a common multiple, so they are cleaning 12 cars. A + B = 6 cars/hr, A + C = 4 cars/hr, and B + C = 3 cars/hr. (A + B) - (A + C) - (B + C) = 6 - 4 - 3 = -2C = -1 car/hr. Solving this. C = 1/2 a car per hour. I used this to solve for A and B, giving me that A cleans 3.5 cars per hour and B cleans 2.5 cars per hour. A + B + C = 6.5 cars per hour. Since they had to clean 12 cars, it comes out to 12/(6.5) or 12/(13/2) which simplifies to 24/13.
oooo smart!
Talking about "percentages" might tend to confuse, since each person's percentage of the task is going to shift once you throw all three into the mix. Instead I went with "Alice's rate of jobs per hour + Bob's rate of jobs per hour = combined rate of half of a job done in an hour (from "one job takes them two hours").
So A+B=1/2, A+C=1/3, B=C=1/4. Same relationships as your equations, but I think more clear to understand. Add them up and get 2A + 2B + 2C = 1/2 + 1/3 + 1/4, change the fractions to a common divisor as 6/12 + 4/12 + 3/12, so 2(A + B + C) = 13/12, thus A+B+C job rate is 13/24 (i.e. 0.542 jobs completed in one hour), which means 24/13 hours to complete one full job.
It's easy to further compute that individually, Alice finishes 7/24 jobs per hour, Bob finishes 5/24 jobs per hour, and Charlie finishes 1/24 jobs per hour. Slacker Charlie tasks a full 24 hours to finish a single task.
Reply from ddichny is more complete, thus more powerful, since it is fully solved. With all terms solved, any hypothetical situational question concerning the performance of these three people will yield exact result with only simple arithmetic. This question can be described as three simultaneous equations with three unknowns. The twist that confuses some readers is that it's a word problem that presents the facts in terms of how many hours to complete the work, but it is solved by recognizing, as ddichny did, that the inverses (rates of work per hour) are used to arrive at the solution. Poster neilw8138 also correctly points out that there are a number of ways to arrive at the correct solution.
charlie is that guy that writes his name on the project but was never there doing it
It's more Bob
What if Charlie upped the quality significantly at a deeper level of analysis, while the cooperation among the three allowed it to be completed at 9 minutes less? yeet
My thinking "Bob is irrelevant, Charlie sucks, the time will be equal to the amount of time it takes for Alice and Charlie, so 3 hours." While I was technically wrong, I feel my answer falls within the spectrum of likely real world outcomes.
Charlie does work too! He would finish the job alone in 24 hours.
Bob is worth 5 Charlie’s
Alice is worth 7
Charlie was fired that same day
That means the answer is 2 hours XD
Two hours. You sideline Charlie, since he's clearly sandbagging whoever he works with.
Same lol, I also thought it was two hours. Turns out it is less than that.
@@nandantandel1604 Technically you're right, since if you round off 1 hour and 51 minutes then you get 2 hours
So if this problem was in a real world situation charlie absolutely didnt do anything
If he only saves 9 minutes of time, he's not worth employing anyway.
@@peppermint1050 Spoken like an engineer
Intuitively, the best way to understand it is by calculating how many times each combination can complete the task in a 12 hour period (12 is a common multiple of 2,3,4)
A+B=6 A+C=4 B+C=3 therefore A=3.5 B=2.5 C=0.5 and A+B+C=6.5 so we convert it back into our 12 hour period: 12/6.5 = 1.846... = 1h50m46s
Lovely maths. In my head I went for between 1.5 - 2 hrs. As I'm used to a time / motion work ethic, Ive forgotten the theory, but logic told me that between them, adding up /×3 to equated to the total you showed. The prime number, the one that all can be divided into is something I didn't think about, but I see the pure maths behind it. Great job!
The job will never be completed. Alice, Charlie and Bob have been working on this same job since I was in school. If they haven’t finished it by now, they never will.
🤣
You are awesome
can confirm we are still working on it
@@Bob-hh8rp 😂
Its cuz when charlie and Bob are together they just goof off and Alice cant do it by herself
Actual Answer: 2 hours. Alice and Bob tell Charlie to sit this one out since he tends to slow them down.
Charlies average is actually closer to Alice's according to the information given. I came up with 4 hours with all 3 of them working to gather. I dont disagree with the fact that working with Charlie wouldnt be the most efficient.
charlie calls them both racist and spends 6 hours in the h/r dept attempting to get the other two fired alice spends 5 hours in h/r with a claim of sexual harassment on both bob and charlie says she wants a raise and promotion and bob spends 5 min dropping off a i quit notice at h/r because he is sick of working with either of them lol
That is the logical conclusion . Charlie can stop others from interrupting the work or "trying to help" . .My first thought was Alice can do it in an hour by herself .
Absolutely.
I was thinking the same thing.
Getting this right in the pause filled me with much needed satisfaction.
Sorry but I have to correct you for a second. As someone who has worked in many group projects, adding more people to the group does not always mean the project will get done faster. Usually 2 people mess around, and one person is left with all the work. This would support the idea that having a group of three individuals would take more time to complete the task.
The person who thought up this question has clearly never been in a college assignment group.
This a question for averge US teenagers
@@insomniac5129 They mean to joke in the "work is constant no matter how many people you put on the job" for this equation.
@@Xeneonic Well I didnt see that lol
Exactly. They probably never left their mothers womb somehow to be precise.
The real answer is 4.5 hours. Alice, Bob, and Charlie are good friends who enjoy each other's company, so when they are working on a task together, it takes longer.
Joe E. I came up with the reason for it taking longer was because they didn’t get along and kept nagging at each other and arguing... 😂
Or they made it to the best quality
"Assume each person works at a constant rate, whether working alone or working with others."
Harvard needs you
Must be friends with benefits then :)
Or you can also use this method:
1/A + 1/B = 1/2
1/B + 1/C = 1/3
1/A + 1/C = 1/4
If you sum up all equation, you will get:
2/A + 2/B + 2/C = 13/12
1/A + 1/B + 1/C = 13/24
Then we can get back to old equation BY RECIPROCATING ALL TERMS
A + B + C = 24/13 hours
I solved this by effectively using the parallel resistance formula: 1/A + 1/B + 1/C = 1/t, solve for t.
I came up with this by realising that, instead of adding the times, I should be adding the speeds. And since speed = distance/time, I set distance to 1 and added. Then, since time = distance/speed, I did 1 over the total and got 24/13. You can use any positive number in place of 1 and it still works.
Fabulous 🎉
What this video taught me, more than anything, is you can use math to get the right answer and still have it be totally wrong in a real life scenario.
When ever you see "assume that" in a math or science problem you can assume that it will be different from a real life setting.
Depends on what real life scenario you're talking about. You're assuming these are people. We could be talking about 3 roombas.
@@misterkite - Dammit, now I want a Roomba so I can name it Alice The Overachiever.
🤣😂👏🏻👏🏻👏🏻👏🏻👏🏻😆
So funny but the wrong initial answer is probably the most accurate. When doing construction In a limited area, more people can just complicate things.
Real life answer is two hours. Alice and bob do the task while dipsh$t just watches
Lol.
i though the same thing. or what if bob did no work. the the answer is 3.
Just depends on who was the "supervisor"
it would take charlie 24 hours to get the job done (ignore my name)
you sir are about to put all the charlies on tilt
My blind answer:
Since we’re dealing with the inverses of 2, 3 and 4, let’s assign 12 productivity units to the job being completed in 2 hours, 8 units to it being done in 3 hours, and 6 units to it being done in 4 hours. From there we can use this trio of equations to work out the productivity of each member, and then combine their productivity and convert it back to time.
A+B = 12
A+C = 8
B+C = 6
A-B=2
2A=14
A=7
C=1
B=5
A+B+C=13
2 hours * 12/13 = 24/13 hr to completion when all are working.
Oh hey, I was right! But I had several advantages. I knew most people get this problem wrong, so I treated it with skepticism, I had unlimited time, and I hold a Bachelor’s Degree in mathematics, so if I can’t do basic linear algebra, or I get the wrong answer because I’m not checking if the answer makes sense, the education system has failed me.
Excellent explanation. Thanks for sharing.
Glad to know I wouldn't do the incorrect method.
Or the correct one for that matter
Yup
Hey at least its progress
Honestly I think most find the wrong answer and knew it was wrong, they just had no idea how to do it right. At least that was me. I only didn't bother to do equations
I got a really close answer using the incorrect method; I did the incorrect variable assignment but set up a final equation A x B x C instead of A + B + C and I got 1.875 hours or 1 hour 52 minutes 30 seconds. Really close
Yeah. I was on the right track but I had the "1" on the wrong side of the equation.
@@waelnawwal it depends on reasoning tho. The wrong method makes no sense at all, even if it cn be described using words. Dw im also a victim of this problem
Here’s my solution:
Bob and Charlie must be dating, so they’re the most distracted when they work together because they’re all lovey-dovey, which is why it takes them 4 hours to finish the job.
Alice and Charlie are close siblings, so they waste an hour or so talking while working together.
Alice and Bob don’t really know each other well, so they’re able to focus more and finish the job in 2 hours.
If all three of them were to work together, then Alice will realize that Charlie and Bob are dating, and she’ll start being very protective of Charlie because she doesn’t trust Bob with him (she’s an overprotective older sister and doesn’t know Bob very well). This will lead to an argument that results in bruised feelings, potentially damaged relationships, and no work done. So they never finish the job.
I’ll take my Nobel Prize now, thaaank you :D
Yup. Accurate!
After that Bob’s friends Daniel and Ethan come in and start fighting and now their relationship is broken which results in stress-working, and now the technical work/h is actually higher. They are now working separate jobs with efficiency. Now the work per hour is higher than Alice, who is sobbing in the corner.
This is dangerously accurate. O.o
@@anantmalik You know, I’m something of a scientist myself.
@@EMLtheViewer Good evening Mr. Emalan. I am almost a scientist. I am a Ph.D. A Doctor in the fields of Management and Psychology. Nice to meet you. :)
I did not figure this out. I am a 58 year old man with minimal education who failed high school math. But I realized almost immediately that the answer must be a little less than 2 and then I got hung up on whether the answer should be expressed as a fraction, or as a decimal.
knowing it is a hard problem helped me think deeper and solve the problem (calculating working speed)
"To the professors' surprise, many of the students set up the wrong equations and could not solve this problem" -- This is a fairy tale. No professor would be surprised by that.
it should be : professors are happy, as they successfully setup those naive student who have too much confidence
Actually, the professor would count them all wrong. The professor would say the correct set up would be to let the government do the task while the 3 workers where on the draw from the government!!
@@vergilw7009 Or 'the professor busted the new students' arrogant & over confident bubble.' 🤔😅😉
At least they know all the 102 genders which is way more important :D
... nor would a professor be surprised that they turned in the resulting (wrong) answer. A more intersting question is: of those who turned in the wrong answer, how many knew it was wrong vs how many didn't even think about it. A follow up question is: of those who knew it was wrong, how many of them actually felt some kind of remorse (as opposed to those who were perfectly content to have something mathy-looking on paper.) Sorry, Mr. Talwalker, but in my experience, concern for the rectitude of one's math homework was non-existent among almost all of my peers -- even at the college level (and even at a highly respected science and engineering school, no less!) My contemporaries were masters at playing to the curve. They'd've seen this problem as a quickie free-bee and moved on as fast as possible.
“More people working on a job should get it done quicker”
The reason most college students get this question incorrect is because they understand that... No.
But that is how that works, if they are for example building/painting a wall. Everybody works on their own part of it without interfering with each other.
@@nesnasimgoogle4580 - in quite a few types of jobs, adding people increases the friction, slowing down everyone. For example, if there are only two paint cans, now Charlie must interrupt Alice and Bob to get paint. Or, at the beginning, extra time is spent to find a new can for Charlie and to fill it for him. Which, in the real world, unless you have excess amounts of paint, someone will run out of paint during the job and will need to interrupt the other two for more paint. The real world is messy; algebraic problems are simplified views of the world where these non-numeric factors are ignored.
see, when the 3 people have to build a house they take less time because one starts with the wall, the other builds the roof and the third installs window and doors. and this makes sense because it is mathematically correct 😌
@@violinyay6632 - What you described cannot all happen at once, because the guy building the wall needs to build it BEFORE the roof or the doors and windows can begin to be installed. Math IS great, but it needs to be applied carefully, taking into account the knowledge of the real world.
@@billb7636 Damn, I forgot that gravity exists again. How does that keep happening?
It's really embarassing.
You should see me trying to build with Legos
Nailed this one! ❤ great channel!
Good video. There are actually several ways to solve this problem. I recommend changing the wording of "The Correct Solution" to "A correct solution" to reinforce the idea that most complex problems have many possible paths to a solution.
The funny thing about questions like these is people always go: "It wouldn't make sense for more people to work on a task and have it take longer." My response is always, "Clearly you have never managed employees."
The problem does state that they work at the same rate regardless of who they work with.
Even ignoring the social psychology issues, most tasks are restricted physically or logistically in how many people can effectively work on them. 3 people can't wash dishes in a single sink, for example. The math problem assumes a very particular sort of task.
Yeah, math never takes decreasing marginal utility into account.
Alice stood around chatting and it still took four hours.
You are welcome.
I found the manager that sits on his/her ass all day and has no idea how to actually do the job or even tie their own shoes for that matter. Plugging in names on a schedule and entering fields on a payroll application is so hard, isnt it?
Insight: don’t involve Charlie in group projects
I just found this video and thought of it in the values of fractions.
Since Alice and Bob can get the job done in 2 hours, it's inferred that together, they do 1/2 of the job every hour (1/2*2 hours = whole job done)
Same goes for the other two equations, if Alice and Charlie take 3 hours to complete the job together, then they do 1/3 of the job every hour. And the last equation, Bob and Charlie take 4 hours to complete the job together and do 1/4 of the job every hour.
I decided to find out what fraction of the job will be done in an hour if all three work together.
Adding all the equations together, 2A + 2B + 2C = 13/12. Divide the whole equation by 2, and you get A + B + C = 13/24 of the job done per hour.
To get the full job done (AKA getting the fraction to equal one), just multiply the proportion "13/24 of job done / hour" by the reciprocal of 13/24, which is 24/13. So, it takes 24/13 hours for all three of them to complete the job together
I just made the job concrete. They had to move 24 boxes. This showed me that Alice moves 7 boxes per hour, Bob 5, and Charlie a measly 1. So in total they can move 13. Then it was just dividing 24 boxes by the 13 per hour.
The "work done per unit of time" is the inverse of the time used to complete the work, so it is possible to just simply solve:
a + b = 1/2
a + c = 1/3
b + c = 1/4
summing up all three equations: 2a + 2b + 2c = 13/12 --> a + b + c = 13/24. The solution is the inverse of it, that is 24/13.
Holy carp this is so elegant it beats the video's "official" solution!
Yes! Much clearer to think in terms of rates.
Also thought of this in terms of rates, starting with making 120 widgets, A+B make 60/hr, A+C 40/hr and B+C 30 Hr. Adding the first 2 together 2A+B+C=100, we know B+C=30 so that means 2A = 70, or A=35 per hour simple maths from then on gives B at 25 per hour and C at 5 per hour or 65 per hour aggregate. 120/65 = 1.84 hrs (1hr 50min 46.15 sec approx.)
Yes, it is easier to assign variables to the entire individual rates, not just the individual hours. Excellent, Michele! I used Substitution while keeping everything as a fraction leaving out a discussion of percentages, which can be confusing for many students. This also was a much quicker process.
I hope you teach Math or Physics or something because your students would be blessed to have you as their instructor.
Easiest solution
Three days. See, Bob has a crush on Alice, but Alice is hooking up with Charlie, which accounts for the extra hour it takes the two of them together and the extra two hours Bob and Charlie spend arguing. If you put all three on the same task, the dynamic totally breaks down, Bob and Charlie both end up in 48 hour lockup and Alice quits because of the 'toxic work environment'.
I smell lawsuit
😂😂😂😂 most logical response yet!
Classic! That is so funny I work with a painting crew and I tell you it is exactly as you explained. I'm the foreman and I get so frustrated because I'll put 2 guys on a job that should take a half an hour and they are still in there 3 hours later! LOL LOL
The real world intrudes again!
Hahaha ....its refreshing to run across a sense of humor similar to my own!
In one hour Alice+Bob complete half the job, Alice+Charlie complete third of the job, Bob+Charlie complete one forth of the job. Adding all that we get that in 2 hours (since each name appears twice) three of them working together complete (1/2+1/3+1/4)th of the job. 1/2+1/3+1/4 = 13/12. Set up a simple proportion: 2 hours corresponds to 13/12 job, x hours corresponds to 1 job, so x=2/(13/12)=24/13.
Woot! I got the right answer...but it took a while, I needed to write formulas on paper, and I was a bit uncomfortable with a few steps such as a normalization step to get say Alice's rate in terms of jobs/hr rather than relative to Bob or Charlie's. Also I was uncertain my approach was right and did time consuming verification math, ending up pleasantly suprised I got it right! I did it an overly complicated way vs the video's solution, but I got precise rates: Alice works at .29 jobs/hr. Bob works at .208 jobs/hr. And Charlie works at .0416 jobs/hr.
As an elementary school teacher intern, I can tell you that more people in a group can DEFINETELY mean the task takes longer to get finished.
🤣🤣🤣🤣
Hope you are not an English teacher.
It depends on the job. Lets say you are cutting a forest down. Would it be longer if you make 2 people do the job instead of 1 ?
@@smurfdurf5625 by your logic, I can tell you that it can take longer, because it also depends on who you are working with. Could be someone who distracts you, and could be a person who will help you
As a retired teacher, I miss the good old days when someone who aspires to educate children could spell common words, especially ones they capitalize.
So Alice deserves a raise and a commendation. Bob gets a warning to improve performance. Charlie gets to clean out his workspace and file unemployment.
Brian Weeks: Best comment! Thanks for a much-needed laugh! 😂😅🤣
Nah, in the real world Bob and Charlie will boast about how they got it done, and Alice was raised to be nice so she doesn't interfere. She's end up with the same salary but doing most of Bobs and Charlies work. Since Charlie was the most useless, he'll be the one getting the promotion in the end.
My version was Charlie wasn't worth paying for 9 saved minutes so I basically had the same reaction.
But if Charlie gets fired, then the equation gets screwed up and we have to start all over again!
Yes, with a little more math it comes out that Alice is 7 times more productive than Charlie & in the project with all three, Alice did 54.8% of the work, Bob did 38.5% of the work, and Charlie only did 7.7% of the work.
I did it in a very different way. Considered that the job can be "240 units of work". Using that, I calculated the "units of work per hour" for each pair, and then calculated it for each individual. Alice can complete 70 units an hour, Bob can do 50, and Charlie can do 10. (240/130)*60 = about an hour and 51 minutes
Boy, talk about doing it the hard way. This is a 20-30 second problem.
"When more people work together it should take less time, not more time"
Sounds like you've never worked in Software development
Sounds like you stole the popular comment
Josef Aguilar
Or had a VP involved.
Oh, wait.
They mentioned work.
You can’t get 9 women pregnant to get a baby in a month
HappyCat3096 How would the 9 women work together tho?
@@HappyCat3096 Yes, you can, but the women have to exist in separate dimensions and then you need a wormhole to combine 9 babies into one.
Well, Alice and Bob have good chemistry together, so they get the job done fast. Alice and Charlie don't mind each other. Bob and Charlie actively dislike each other, so when they all group up to get the job done, Bob says: "Charlie, no offense, but me and Alice alone would get this done faster than if you weren't here, so go do something else."
2 hours.
Alice and Bob actually finished the job in 1 hr 55 mins. But they clocked at 2 hrs just so they can beat Charlie up for 5 mins straight
This is exactly how it goes in the real world.
Except the beating.
It's a lot more fun to watch Charlie struggle for 5 minutes trying to tie his shoes, only to finally manage it and realize he put them on the wrong feet.
I definitely read it as Bob and Charlie were buds and just goofed off the whole time.
@@datphung8656 I died laughing at this and the comment above.
@@frisbeedan8905 Yes; me too. Charlie is a fun guy and even Alice laughs when she works with him.
people get this wrong because they memorize formulas without understanding them. thank you for the great tutorial.
this one was tricky, love the vids
Calling the problem "basic" is an overstatement. The problem itself is tricky unless you take context into consideration, but schools do not teach this, especially in math. Students learn systems of equations, but are taught to solve problems like this as simple equations rather than worry about percentages.
I think the main issue isn't that college students can't solve this "basic" problem, but rather schools don't prepare students to solve problems like this correctly. In math, most students don't think about the context of the problem itself, but rather patterns in the problem and using equations and formulas to solve it.
can confirm, in calc 3. the extent of word problems is physics and that just supplies variables to use in memorized equations
Sry If your school was like you said. I learned in school to think before calculate, what could be a solution, and after calculation, can this solution be right.
Ok.. I plugged this into Wolfram Alpha: Alice is 7/24, Bob is 5/24 and Charlie is 1/24. Charlie should save 10 minutes off the job (1/12 of 60). It’s almost like an “are you smarter than a 5th grader question”. But I do agree though, schools teach too much by rote.
Not idea where u studied, but at my highschool I have done many problems like this in classroom lmao. it actually surprise me that college students are having problems with this kind of basic equation.
As a college student, this is definitely very true
I had a simple answer: Charlie slows people down, so he needs to sit back and let Bob and Alice get it done the fastest, in 2 hours. We also just have to keep Bob focused because according to his work with Charlie, he gets distracted easily and takes the longest in the combo
hahaha exactly, I think so too
Charlie doesn't slow things down he just works more slowly but is still making progress, not slowing it. Letting Bob and Alice do it alone is 9 minutes SLOWER than if Charlie helped.
As somebody who used to work in retail management, this is the correct answer. Charlie should be assigned to a different task that will allow him to work at his own pace or one that doesn't have to be perfect, but is repetitive, and he can rush through to get it done.
@James Ratliff Alice should work alone instead.
Charlie had special needs and discrimination will not be tolerated. Now Alice and Bob both lost their jobs because Charlie viewed Alice and Bob's comments about "working too slow" as harassment. Now the whole operation is run by Charlie. Moments later, everything has been outsourced to a disadvantaged country to avoid bankruptcy. Everyone loses their jobs, and Charlie is the only one qualified to receive social assistance because he has special needs.
Best way is for Alice and Bob to tell everyone else to bugger off as it's almost quicker without them.
I immediately knew the answer needed to be lower than 2 hours but I didn't know how to get there. really shows that I haven't done much math since I graduated 16 years ago
What I learned is that Alice is the GOAT and Charlie’s illiteracy has screwed us again
Yeah sure whatever but how much do you know about bird law hmmm?
Well, uh... Fillibuster?
Then Go Away! ,Finally!
Bib’s the GOAT too.
Charlie don't surf, but we think he should.
4.5 hours is entirely believable - I've worked with people on teams who actually slow the whole team down - also, the Mythical Manhour explains how adding more people to a problem can actually make it take longer
😂😂😂 like group study
Yeah, anybody that has worked anywhere would not have questioned that conclusion. It would have been more like, oh wow the math is actually accurate to real life for once.
Yes but they have to work at constant rate
exactly what i was thinking
If you want to get something done quickly give it to somebody who is busy 😀
I got this right, but I did it differently. I set this up as a system with the equations x + y = 1/2, x + z = 1/3, and y + z = 1/4, since that's the amount of progress each pair will make in one hour. You end up with x + y + z = 13/24, which is the amount of progress the three would make in one hour. Therefore the answer is the reciprocal, 24/13.
In india we are always taught to calculate using 1 hour's work i.e the work done in 1 hour which is in this case is 1/2, 1/3, 1/4 respectively. I did it this way and got the answer correctly.
Now seeing your video it makes sense why we used to take 1 hour's work instead of the actual time taken.
Thanks folk! 🙂
However you have to do the reciprocal of the answer obtained in order to get the time because it's just the part of work all three could do in an hour.
"A common mistake is that students turn the names into variables and turn the sentences into equations..."
* quietly crumples paper before shoving it into my mouth *
I made that mistake...then I made another mistake. I finally settled on a third mistake.
I hate to admit that I was so sure about myself that I almost didn't click on the video to check the answer.
@@Armando2609 I feel ur pain man, 4.5 gang where u at 😎💯💯
Well I'm not a man :P
@@Armando2609 its an expression not a statement bro 😎👍
If Charlie was left at this alone, he would take a full 24 hours to finish the job. Poor guy.
If charlie was left alone he would quit or kill himself because he's a career underachiever.
I got to the same answer a slightly different way. I started here:
a+b = 2
a+c = 3
b+c = 4
Then i simply divided 100 (basically as in 100% of the job) by these numbers.
a+b = 50 (because 100/2)
a+c = 33 (because 100/3)
b+c = 25 (because 100/4)
These numbers are essentially work rates. But I need them for each individual, not just the different pairs.
a + b = 2(b+c)
a = b + 2c
a = 25 + c
I now have a in terms of c, which means:
a + c = 33 can be written as
25 + c + c = 33
2c = 8
c = 4
a = 29
And since a + b = 50, b = 21
a + b + c = 54 (which basically is the trio's work rate, in % per hour). To do 100% of the job, they need:
54x = 100
100/54 = 1,85
1,85 x 60 min = 111 minutes = 1h 51min
I found it pretty smooth. What do you think?
Man I got so close, I got far enough to realize you had to think about the variables as percentage of the job done but I wasn't sure how to write it out. Dang
Charlie really is not contributing much, is he? Barely 9 minutes time save over two hours if he helps Alice and Bob
Alice is the real MVP here
How did you work out that charlie only did 9 minutes i don't get it
Alice+Bob= 2 hours
Alice +Bob+Charlie =1 hour 51 mins.
The time was decreased for 9 mins when Charlie worked with them..
@@waraulhasan2477 XD
Work rate per hour for the individual persons:
Alice: 7/24, so she would perform the task in 3 and a half hours.
Bob: 5/24, so he would perform the task in slightly less than 5 hours.
Charlie: 1/24, so he would perform the task in 24 hours.
Lay off Charlie he's a show learner and new to the job! But one he gets going..
I looked a the original equation and said "two hours. Anne and Bob will do it and Charlie will go get them all coffee".
This is the REAL LIFE answer !! :)
I said less than 2.
Yeah definitely Considering for the fact that charlie only took off 9 minutes out of 2 hours.
but wouldn't the coffee make them work faster?
@@fnutarf2085 you assume it would take Charlie less than 1 hour 51 minutes to get them that coffee.
The correct set of equations become apparent once you recognize this to be a constant work-rates problem and basically the concept of amount of work in some units of time is what controls everything.
It lead to the same answer, but I thought about it slightly differently. I thought of Alice and Bob completing the job in 2 hours as A + B = 1/2, because they work together at a rate of 1 job every 2 hours. And so on.
I used the same method. Just have to remember that when you solve for A + B + C this way, it will give you 13/24, which represents the jobs/hour. So you have to remember to take the reciprocal (i.e. 24/13) in order to get the answer, which is supposed to be in hours/job.
"It should take less time with more people helping." As someone who works in a large corporation, I laughed at this claim.
I too see this every day. This question does not define the type of work. 4.5 hrs could be correct depending on the type of work. Since we don't know for sure, the answer should be impossible to determine without more information.
LOL, yeah been there done that, once the slackers realise they can sit on their butts, the jobs always take longer but the slackers get promoted LOL!
Its the same logic as 9 mothers can give birth in one month
Yep - people will argue and take more time - I thought that was the trick of the problem.
Just because it should, doesn't mean it will. Sadly enough.
Real world answer: Alice is an ISTJ and can get the job done in one hour if the other two, and everyone else, would just leave her the hell alone.
@@tarico4436 Random misogynistic incel comment right here folks, *claps*
How's therapy going?
@@tarico4436 YIKES
I never heard of ISTJ before, I read about it and it sounded like me (which I expected after this comment). So I took an online test and it told me I'm an INTJ, I wasn't sure which one fits more to me so I did another online test and again ended up as an INTJ. But I still think that depending on the situation I'm something in-between.
Yeah, based on those numbers, Alice can do the job alone in 3.5 hours (which is less than the other two together), Bob can do it in about 5, and Charlie left to his own devices would need 24 HOURS!!! Let the woman do her thing!
This reminds me of a similar exam question I had to face during my time at school:
"There's a gargoyle spouting out water at a fountain filling up a basin, and it has three spouts: its left and right eyes, and its mouth. The left eye by itself needs two days to fill the basin completely, while the right eye needs three days. If all three spouts are running, the basin is filled in 24 hours. How long does the mouth need to completely fill the basin?"
The difference is that "my" problem was in a context of fractional terms, but the way of solving it is similar to here, and solving the one from this video had me thinking similarly in the sense that A + B = 1/2.
I did manage to work this out exactly the same way that you did .. but did think, along the way, that if Alice and Bob take 2 hours and Alice and Charlie take 3 hours that means that Charlie is working at a slower pace than Bob is, and if Bob and Charlie take 4 hours that means that Alice seems to be doing most of the work.
The first answer makes perfect sense if you are contractor.
- "How long time will it take?"
- "It will take two hours for me to do it. If you want to help, it will take four and a half hours."
And if you want a govt grant/blow out your budget, and take a couple of years, put together a committee and we'll get right on it.
Way to make a problem way more complicated than it needed to be.
Convert from times to rates: A+B=1/2; A+C=1/3; B+C=1/4 [all in jobs per hours]
Add up both sides of all three: 2(A+B+C)=13/12
Simplify: A+B+C=13/24
Convert back to time: 24/13 [back to being hours]
Yep, much simpler. The maths is technically identical, but much easier to understand each of the subsequent steps after you make the initial conversion.
Yes, jobs-per-hour is the key concept, gives 3 equations for 3 unknowns, better to solve them as such, rather than looking for a trick, in this case adding all 3 equations, which works in this example, but might not work in other examples.
@@climanrecon5649 well adding all 3 equations is just a shortcut to forming a quantity proportional to A+B+C. In either method it could be done by individually solving for A, B, and C, but that's more work than is necessary
This was the way I did it, the part of the question saying “assume all work at a constant rate” saved me from falling into the A+B=2 trap
@@thomasr5302 Assuming constant rates is a good clue, but it leaves out a critical assumption: that there are no interactions (in the statistical sense). In other words, we must also assume that each person works at the same rate regardless of who else is working with them. As a real-world counter-example, my guess is that it would take the three of them about 24/7 hours to do the job as a trio, because Alice would end up doing everything while Bob and Charlie worthlessly compete for her attention.
In every job, programming included, there is an optimum number of workers. This varies with the experience levels and how much supervision each person needs. But there is always a level when you have too many workers, or too many at the wrong level. This problem is assuming that you don’t have too many, although it is obvious that Alice is carrying the biggest part of the job.
My approach gets the answer only using fractions rather than percentages. It works as follows
Let A = The time it takes A to do the job alone, So the fraction 1/A represents the fraction of the the job done in 1 hour( example if A took 2 hours he would get 1/2 of the job done in an hour. Etc for the others. It seems more natural for me.
then 1/A+1/B =1/2, 1/A+1/C=1/3 and 1/B+1/C=1/4 so then find t so that 1/A+1/B+1/C=1/t
So the rest adding 2(1/A+1/B+1/C )= 13/12 dividing by 2 bth side gives you
1/A+1/B+1/C=13/24= 1/(24/13) so t = 24/13 hours.
Yep i did it this way in my collage
Wow bro, this makes way more sense
My daughter, when she was at UGA, found it saved time when assigned a group project, to just say she would do the entire project herself. That was after a group she was in was unable find time to meet together to finalize a report, so she had to complete everyone in the group’s assignment the day before it was due. The person who commented that Alice could have done it faster if the guys would just get out of the way was right.
I detested group projects. One professor had us anonymously submit grades and evaluations of the other group members. My group was three women and a VGL guy who always made sure we knew he was going to be late for a date because of our meetings. I was the only one who submitted an honest evaluation. The professor gave the women As and Casanova a B. Everyone was shocked and wondered why. 😈
Pretty much
My daughter was a straight A student and she hated it when teachers assigned assignments to be done in a group because other students never did any work they just fooled around and she ended doing the whole thing to just get it done. She always carried the load and the others took advantage of the situation and got a better grade thanks to her efforts. Most students have a very poor work ethic and never get down to business to complete anything.
@@patsmith5947 But this is exactly how the real world works. The reward for doing your job well is always getting to do somebody else's job and if you don't know who's job you're doing....somebody is doing yours.
Go Dawgs!
Imagine paying Charlie's whole salary just to save 10 minutes. Guy must be friends with the boss or something.
He’s is clearly an intern that has newly arrived...
Say there were 100 people working on the project. That 10 minute early completion time now means 1000 minutes of man hours saved (assuming everyone needed to be working for the full duration), so there are some cases where it could be beneficial!
9
@@mrksgb8607 not possible, new interns can only slow down tasks
Source: currently a new intern
If I had to guess, I would say he's the owner's nephew who just graduated High School and needs to pay rent to his Dad. Just don't tell any of the other employees.
I've encountered this type of question in olympiads before, so I kinda know a formula on how to do it:
if A and B do something in x hours, then you can basically say: 1/A + 1/B = 1/x, as long as A and B remain constant the whole way through.
So in this case... we get these 3 equations:
1/A + 1/B = 1/2
1/A + 1/C = 1/3
1/B + 1/C = 1/4
add them all... you get:
2/A + 2/B + 2/C = 13/12 (divide both sides by 2)
1/A + 1/B + 1/C = 13/24
Make 13/24 into 1/x, you basically get 1/(24/13)
Which means that together, they work for 24/13 hours, 1.85 hours, or 1 hour and 51 minutes.
Anyone who thinks the job taking more time with more people doesn't make any logical sense has been really blessed in the quality of people they work with.
It will take 2 hours . Alice will do the work, Bob will help and Charlie will watch. End of story.
Alice will do most of the work, Bob will help somewhat but mostly get in the way, Charlie will spend the two hours taking credit and brown-nosing the boss and will get promoted before Alice or Bob. Then he'll continue to give them all the work.
Alice and Dilbert (Bob) work together while Wally (Charlie) drinks coffee and reads the newspaper in his "office." After much labor the PHB informs Alice and Dilbert the project was cancelled a couple of months ago due to a reorganization. So Wally turns out to be the only winner here...as usual. So C>(A+B) and PHB
It just takes one hour for Alice to finish the work alone.. The other two douchebags are slower..
@@pragalpaah4314 Of course!. If Alice is alone, she doesn't get distracted. If she works with any of them, she does. Don't you see the problem? Is called hormones.
Alice and Bob will do the "work." Charlie will watch.
Fixed your story.
"Now, before I solve this, let me talk about a common mistake. Many people see the first line and translate it to A+B = 2." -> Sad me looking down on my paper. First line: A+B=2
Me too😄😄
Saaaaame 😭
Yep, same 😞😁
Ha, I fooled him, I had X+Y= 2
Same
A more intuitive way to explain it is to convert to speed.
A + B = 1/2 job per hour, etc.
Then use Matrix reduction, substitution, or whatever your preferred method is to solve for the speed variables. Then add up all the speeds and inverse for time.
The method shown in the video seems arithmetically easier, but not a simple to wrap your head around.
Easy solution:
since, X =>2hrs for 1 work, ∴ x = 1/2 work per hr
so we can just reciprocate...
A+B=1/2 --①
A+C =1/3 --②
B+C =1/4 --③
since, eq1+eq2+eq3 = 2(A+B+C)
(A+B)+(A+C)+(B+C)=1/2+1/3+1/4
2(A+B+C)=1/2+1/3+1/4
A+B+C=(1/2+1/3+1/4)*2
A+B+C=(13/12)*2
∴Work per hr=13/24
thus, work = 24/13
now in terms of hrs & mins;
24hr 4min (approx 4 min)
Even before doing any math, I can safely say Charlie should probably be fired. Bob is probably an average worker, and Alice should probably be promoted or given a raise.
No, Alice's reward is more work with no raise. That's how things work. And Charlie gets promoted to manager.
@@rodicow3491 That is the way the real world works, the real worker gets all the S@h@t rolled down on himself while the others get praswd and paid more to do less work.
@@rodicow3491 sounds like Charlie is the son of someone in upper management.
@@piranhaplantX Or the manager's friend from church/book club etc. We've all worked with the type XD
Charles is the intern.
I'm guessing Charlie is the son of the owner and gets promoted to manager, Bob gets promoted to supervisor and tries to employ as many Alices as he can find to get the job done.
Bingo, real world answer.
Good, I need a job.
MACKENZIEEE
This solution is easier for me:
Change hours per work into work per hour (wph for convenience) to get
A + B = 1/2
A + C = 1/3
B + C = 1/4
Now solve:
A - B = 4/12 - 3/12
A = B + 1/12
B + 1/12 + B = 1/2
2B = 5/12
B = 5/24
A = 5/24 + 1/12 = 7/24
C = 1/4 - B = 6/24 - 5/24 = 1/24
Now consider
7/24 + 5/24 + 1/24 = 13/24 wph
1/(13/24 wph) = 24/13 hpw
They are doing 1 work, so
(24/13 hpw) * (1work) = 24/13 hours
You're telling me that Charlie saved a measly 9 minutes in a two hour project...
He might be in training
@@potato1341 or maby he isnt a team player so the whole team wil loose time for completing the work
I've known Charlies who added minutes to the project...
My name is Charlie ¯\_(ツ)_/¯.
@@greenjelly01 dude i died laughing 😂😂
In my experience, the "wrong" answer is actually closer to the truth, both in school, and in the work world.
Group dynamics would be in play here. We don't know how this will affect the production of each person. Common math sense however told me it would take less than two hours.
One hour and 51 minutes is the answer??? Seriously? Charlie saved Alice and Bob 9 minutes? Is this real math?
Influence of additional communication channels.
Yes. It is more of a litmus test than an IQ test.
@@ritabook5335
Yes! Charlie is that worthless!
It’s amazing that you can find all this questions that exactly 99% of people can’t solve, and that in all your different videos, is there a list of those questions somewhere ?
As a high school student on a robotics team i will say that like everyone else has said, more people can often lead to less productivity lol. It depends on the scenario though! Like we were building a swerve module last Wednesday and there were three people participating but two others who had nothing to do. Some tasks only need one person, other tasks need a whole bunch.
Anyway this was really interesting! I also chose to take the route of a+b+c=2+3+4, until I realized it didnt make sense.