# Most US College Students Cannot Solve This Basic Math Problem. The Working Together Riddle

Hey, this is Presh Talwalkar. Alice and Bob can complete a job in two hours. Alice and Charlie can complete the same job in three hours. Bob and Charlie can complete the same job in four hours. How long will the job take if Alice, Bob, and Charlie work together? Assume each person works at a constant rate whether working alone or working with others. This problem has been asked to students in US colleges. To the professor’s surprise, many of the students set up the wrong equations and could not solve this problem. Can you figure it out? Give this problem a try and when you’re ready keep watching the video for the solution. Before I get to the solution, let me go over a common mistake in how students get to the wrong answer. They read the first sentence, that Alice and Bob can complete a job in two hours, and translate the names and the numbers into an equation. They say this must mean that A + B=2. They look at the second sentence, that Alice and Charlie can complete the job in three hours, and they similarly convert it to A + C=3. The third condition, that Bob and Charlie can complete the job in four hours, gets converted to the equation B + C=4. The question of how long it will take for all three of them working together gets translated into the question

of “what is A + B + C =?” So to solve this system of equations… They want to solve for A + B + C, so they can add up all the equations together. We end up getting two terms of A, two terms of B, and two terms of C, to equal 2 + 3 + 4. If we group the factors [summands], we get

2A + 2B + 2C=9. We then divide by two and that gets us to A + B + C=9/2=4.5 (four and a half). So evidently this will be the answer that many students get. They would say that it takes 4.5 hours for all three of them, when working together. But let’s think about: does this answer make any sense? We know that Alice and Bob take two hours, Alice and Charlie take three hours and Bob and Charlie take four hours, but somehow when all three are working together they take four and a half hours? This makes no sense. When three people work together it should take less time then when only two people work together! But 4.5 hours is more time, so this answer must be wrong. Not only were the equations set up incorrectly, but any student who submits this answer is not thinking about whether the answer makes any logical sense. So how do we solve this problem? We need to set up the equations in the correct method. We know that Alice and Bob can complete a job in two hours, so how do we translate this into an equation? Well, if they complete the job in two hours, that means the percentage of the job that Alice does in two hours plus the percentage of the job that Bob does in two hours equals 100%, or that equals 1. Now since they work at a constant rate, we can say the amount of the job that Alice does in two hours is 2 times the amount of the job that she does in one hour. And the same thing goes for Bob. So we now have a natural choice for our variables we can say the percentage of the job that Alice does in one hour will be the variable A, and the percentage of the job that Bob does in one hour will be the variable B. This leads to the equation that 2A + 2B=1. And that’s how we can translate this we can group this out to be 2 times (2x) the quantity A + B=1. So we can now translate the second sentence. We have Alice and Charlie completing the job in three hours. This will translate into 3 times the quantity A + C=1, where C is the percentage of the job that Charlie completes in one hour. We also have that Bob and Charlie can complete the job in four hours, so that would mean 4 times the quantity B + C=1. Now we want to figure out… What would happen if they all three work together? So we are needing to solve for… the time (t) x (A + B + C)=1. We need to solve for this variable “t”. So how do we do that? Well, we can similarly add up all the equations But we have different quantities of each of these variables, so in order to get the same number of each variable, we’re going to do a little trick. We’re going to multiply each equation so that there’s a leading coefficient of 12, which is the lowest common multiple of 2, 3 and 4, so the first equation will multiply by six. This will get 12 times the quantity A + B to be equal to 6. The second equation will multiply by four and the third equation will multiply by three. We can now add up all of these equations We’ll end up with 12A (2 times), 12B (2 times), and 12C (2 times), and this will be equal to 6 + 4 + 3. We can factor out the 24 of each of these variables, and that will be equal to 6 + 4 + 3, which equals 13. We now divide by 13… and we end up with 24 divided by 13 times the quantity A + B + C=1, and THAT is what we wanted to figure out. So we go back to our setup and we can see that we get to the answer of 24 over 13. So the job will take 24 over 13 hours or about 1 hour and 51 minutes. And this is a sensible answer because it takes less time than any pair working together. Did you figure this out? Thanks for watching this video; please subscribe to my channel. I make videos on math. You can catch me around around my blog, mindyourdecisions, that you can follow on Facebook, Google+, and Patreon. You can catch me on Social Media @preshtalwalkar and if you like this video please check out my books! (There are links in the video description.)

4.5 is now pronounced "four fifths" (2:19).

24/13

My mind after 10 seconds how explain what the correct answer is:

Pues que pendejos jajajaja

It's not correct !! Because Alice does the job in 1/2 hour alone.

Thank you. It took me one hour to understand it. Had to translate it in german and has to write an h after 12 to understand it. Thank you 🙏🏻

I was so close…

No i cant figure it out

I worked it from a business owner perspective.

I used the number 7 as a job to get done.

then I used

Alice = 3

Bob = 2

Charlie = 1

-3-2+7=2

-3-1+7=3

-2-1+7=4

-3-2-1+7=1

pretty simple

and now I will fire charlie and tell Bob to pick up the slack.

Dude, it is very simple. Take average of each job per person per hour and sum all the average. Now divide 1 by average numbers arrived. You will get the answer. Charlie, you are not efficient worker. You are fired.

So how much they will be paid ?

First of all how many college students can read comprehend retain information and problem-solve

Fantastic! Still unable to believe I just made $1193 with this terrific site here no1profits.club?379

Solved in 5 sec.

Im in 7th grade, for me, math is currently easy, but I still hate it.

(no flame war please)

So easy

That is the first or second task that i was able to solve from this channel by myself

I did a different working out and got the same answer of 1.85 hours.

This is a rate(R), quantity (Q) and time(T) problem, where

R = Q/T.

Since the quantity is 1 (one job), then the rate of work of teams:

A + B = 1/2

A + C = 1/3

B + C = 1/4

Adding both sides:

A+B+A+C+B+C = 1/2+1/3+1/4

2(A + B + C) = 1/2 + 1/3 + 1/4 2(A + B + C) = 13/12

A + B + C = (13/12) X (1/2)

A + B + C = 13/24

(Which means that the RATE OF WORK of team A + B + C equals 13/24.)

Since T = Q/R then the TIME it took for team A + B + C to do the job is:

T = 1/(13/24) = 24/13 hours

(which is about 1.85 hours or about 1 hour and 51 minutes.)

Someone can suggest me calculus book for best teaching .

High School to College level.

Please please help me

24/13about1.85hours

I think it should not be equal to1. which you make the job and time the same unit.

I am so happy because I tried to solve this question when I saw the thumbnail and I succeeded .

So…Alice does all the work while the boys stand around with their dicks in their hand watching Alice bend over….

Sounds about tight !!

no…no way….makes no sense

😅 I am a 12 th student and I answer it correctly in time less than 1 min but I do not use percentage concept but another and I get 24/ 13.

The right answer is 2 cuz Charlie lost his job after the 4 hours

Wth they calculated the median of something wasn't asked

Fire charlie, he's a slacker n is dragging everyone else down

I did it this time

I got it in one shot

Who is charlie?

I had this problem in my primary maths syllabus, and yeah I solved it the moment I saw this problem…

Clearly, Charlie is useless.

The question should have been, if you were the boss, who would you fire first?

3 is a crowd and hence take more time.

4.5 hrs

1.85hrs

It's a Seventh Grade math problem in India, of Time-Work Segment

Couldn't you have done it in an easier way😕😩

Hell yeah this is the fisrt time I succesfully solved your problem!!!

This was actually quite easy. I am an 8th grader from Bangladesh and I could solve it.

I mean, I got the most illogical answer but why would we be talking about logic if in the question it has been thrown out the window?

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. Off by 2.5 minutes!!

If I had this on a test, i wouldve gotten 4.5, seen that it doesnt make logical sense, and try to divide it by like 3 or do something to make it less than 4.5

Alice = 0.5 hr

Bob = 1.5 hr

Charlie = 2.5 hr

Problem can be solved by taking the total units of work as 12(LCM of 3 4 and 2 ) and deriving the equations

Its an easy one for 12 yr old in India…

It is one of the easiest questions of "Time and work". It can be solved orally in 5-10 seconds.

I do not know why it was hard for students because I just ended the primary school and I was able to find a solution in 1 minute.

Charlie would take 24 hours to complete the job on his own.

Alice is as efficient as seven Charlies.

2(A+B)=1 and (24/13)(A+B+C)=1,

Substitute A+B=1/2 into the second equation.

(24/13)C+12/13=1

(24/13)C=1-12/13=1/13

24C=1.

Also, (24/13)A=1-6/13

So (24/7)A=1

Alice has a good work ethic. She’s going places.

my answer was 4.5cm

Maybe the three of them don't get along very well

In reality Alice and Bob will finish the Job in two hours.

3:07 so im supposed to believe that Bobby ate 27 watermelons?

So much hate on Charlie ;-;

I figure out the answer 1.84 hours within 1 minute…

Yea i did it without watching the solution 😂

Performance review:

Bob gets to stay.

Alice is 40% faster than Bob, she gets a raise.

Charlie only produces 1/5th what Bob does, and 1/7th of what Alice does. But his daddy goes golfing with his boss, so he gets promoted to management.

Yes…in jst few seconds

I answered this in 20 second, finding for each one how many hours they work, then additionning the results ( but yes, that don't make a lot of sense ).

Charlie : 2 hours and a half.

Bob : 1 hour and a half.

Alice : half a hour.

i did A-B-C= 0.5

I made the wrong solution ;-;

I'm such a dissapointment ;-;

Another solution which is easier to understand:

In 12 hours:

A & B completed 6 jobs

A & C completed 4 jobs

B & C completed 3 jobs

Sum that up:

2 A, 2 B and 2 C completed 13 jobs in 12 hours

Which means:

A, B and C completed 13/2 jobs in 12 hours

So:

A, B and C completed 1 jobs in 12/(13/2)=24/13 hours

So, Charlie is pretty much useless. A follow up question would be how long does each person complete the job alone.

We know ourself as

ASIANSOthers think we are

MATHEMATASIANSTBH I TOOK NOT MORE THAN 15 SECONDS TO SOLVE THIS WITHOUT USING ANY DEVICE OR WRITING OBJECT.

Or you can find the mean which is 3 hours

A+b=1/2, they complete half a job each hour

Alice + Bob. – 2 hours

Alice + Charlie – 3 hours

Bob + Alis. – 4 hours

—————————————-

By taking the LCM of 2 ,3,4 is 12

So let our total unit of work be 12units

Now we will take out individual unit of work.

Alice + Bob = 12 units/ 2 hours = 6units per hour.

Sumilarly ,

Alice + Charlie =12/3 = 4 u per hour

Bob + charlie=. 12/4. = 3 units per hour

—————————————————————-

Adding all the Three we will get

2( A+ B+ C ) = 6+3+4

Therefore In one hour all three will make

(A +B+C) =13/2 units

So to complete total work i.e 12 units they all will take

(A+B+C)= 12units

—————

13/2

So our answer will be 24/13 which is 1 hour 51 minutes.😃🇮🇳great work presh Sir

It really depends on the details of the job. There's no necessity that the work must be "additive," so "working together" gets "more accomplished" in some predictable way.

Here in INDIA this is a group D exam question? Basicaly taught in class 5

Just woundering I used the first step in the wrong approach, but instead I solved for the time variable and found the mean which also equates to 1 hour 51 min, was this just by coincidence or is this and approach that would be deemed correct? Beat regards and thanks for the good explanations

24/13 equals 1.846 i.e. 2.24 hours. Then how did you get 1.51 hours?

This assumption is unrealistic.

Very rarely, the third person will not disturb the work of the others. Often this person has NOTGING TO DO. But let us assume that we have such special work.

The easiest way to solve this is by measuring the "speed of work". With your unrealistic assumption, the work speeds add up.

A + B works 1 Job / 2 hours = 1/2 Job / hour

B + C = 1/3 Job / hour

A + C = 1/4 Job / Hours

2 * (A + B + C) = (1/2 + 1/3 + 1/4) [Job / hour]

So they will do the work in 1 / (speed of work)

1 / (A + B + C) = 2 / (1/2 + 1/3 + 1/4)

Simple multiply 2 x 3 and divide by 4

You need to make the addition between the hors then multipliate by 2/3.

I said 1 but guess in math you Need to be precise and show how you get your answer

To quote my great grandfather in reference to kids helping put up hay, "When you got a boy, you have a boy. When you got two boys, you have half a boy. If you got three or more, you just ain't got no boy at all" (as if to say the more boys that are "helping" the more talking and less work actually happen).

So, by Poppy Carnahan's logic, the first answer of it taking Alice, Bob, and Charlie taking 4.5 hrs to complete the same job that Alice and Bob could do in two, is actually more correct! 🤣

just take the LCM of 2,3,4 which is 12.

So assuming 12 work should be done by them in which (A+B) do 12/2 = 6 parts, (A+C) do 12/3 = 4 parts and (B+C) do 12/4 = 3 parts.

Together they do (2A + 2B + 2C)= 6+4+3 = 13 parts in one day.

Thus (A+B+C) = 13/2 parts in one day.

So total time taken by (A+B+C) = Total work divided by parts of works done in one day.

12×2/13 = 24/13 ans.

Got it right 👍

1hr 51.12 mins or 1.852 hrs

i got 0,5 hours using elimination processes

Just solved in 30 second orally 😄😄

Why bother with Charlie anyway?

If you got 4.5 then your IQ is 4.5

Wrong answer bro it may be 40 are 2 hours 5 min .my answer is 40

Easy one

Maybe For the first time, YES, i figured it out

Interestingly enough I used a dummy variable of 12 Towers Completed = 100% of the Job done. I made an imaginary assignment to de-abstract the problem as much as possible. The assignment was to build a Castle. Each castle consists of 12 Equally Sized & Equally Dense, & Equally Shaped towers. The underlying assumption to be made is each of Alice, Bob, or Charlie will always build any of the towers at their same (individualized) rate. That is, while Alice may not build any of her towers at the same rate as Bob, Any Tower Built by Alice will be at the same of any of her future or Past – built towers. I ended up starting with the equations like 2A + 2B = 12….. And I never defined the unknown, t, as a variable or even listed. I simply realized that the leading coefficient, n, such that nA + nB + nC = 12, would be the Answer. I.e. I didn't define it as n, either. But what should I expect since I did this with Plain old Air Chalk.

-Alice 30min

-Bob 1h30

-Charlie 2h30

-So in theory it makes 4h30

……

Anyone used the parallel resistor formula to solve this?

I figured it out this way.

I set the job as laying 120 bricks. (LCM X 10)

I figured that Alice works fastest so she should do over half the job when she works with Bob. I guesstimated the number as 35 bricks per hour to see how it works and it worked.

If Alice can lay 35 x 2= 70 bricks, Bob would need to lay 25 X 2 = 50 bricks totalling 120 bricks [70+50 =120]. Job completed in 2 hours.

In 3 hours Alice lays 35 x 3 = 105 bricks, so Charlie must lay 15 bricks in those 3 hours to total 120 bricks [105+15 = 120] . Therefore, Charlie can lay 5 bricks an hour.

Now to check out if it really works, I use the speed for Bob and Charlie to see if they can really complete the job in 4 hours and they did.

In 4 hours Bob lays 25 X 4 = 100 bricks while Charlie lays 5 X 4 = 20 bricks totalling 120 bricks [100+20 = 120] Job completed in 4 hours.

So given the above, Alice, Bob, and Charlie together can lay 35+25+5 = 65 bricks per hour.

There are 120 bricks in the job so it will take 120 bricks divided by 65 bricks per hour to get the result 1 and 11/13th hours.

I could solve it very easily. Thanks sir

I figure it out in 2min,

Ohh my god maths is soooo complicated

You can do it more simply by assuming some total work which has to be done as a common multiple of time values

It still doesn't make any sense , A+B completes in 2 hour , but if all three works together they save just 8 minutes? C is just doing 8 minutes of work? If yes, I am not hiring him

Finally we'll explained thank you🙏🙏🙏🙏🙏🙏🙏🙏🙏so much 👏👏👏👏👏