# 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

## 100 thoughts on “Most US College Students Cannot Solve This Basic Math Problem. The Working Together Riddle”

1. CQUNC says:

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

2. Marc Nordengreen says:

I did this in algebra 2 last year but tbh I forgot how to do it, shouldn’t be hard to figure it out tho

3. Pillow Gaming says:

Charlie took 9 minutes to write his name on the project. Dammmmmmnnn thats slow

4. Connectid Tech Talks says:

I got 1.846153846 hours and thought there was no way I got it correct, turns out I did!

5. I'm just saying says:

Unless Alice, Bob and Charlie are robots,
Reason: Human factor
Same trick question with: If a person is running 4 mph constantly, how many total miles the person would cover if he ran for 24 hours straight?

6. Xander LastName says:

Ok so Im tsking a wild guess becuse my mobile data is so slow I can only see the thumbnail. so if alice does 30 minites of work, and bob takes hour 30, whih means charlie taked 2hours 30 and for some reason adding more peopke decreases efficiency so im saying 4 hours 30 final awnser

7. Samruddhi Saoji says:

This is a common question in 9th grade cbse exams

8. Steve Mack says:

Pay Alice overtime and have her do it alone.

9. Camelot says:

This is correct, but only in theory.

10. Nissim Levy says:

Easy question when you notice that adding all the people together produces two of each

11. Kartik Kalia says:

These videos are huge ego booster for me

12. Brett Harris says:

It would have been at least 4.5 hrs. Clearly, Charlie makes mistakes and Alice and Bob have to fix them as well as do their own. Dammit Charlie.

13. Yugal Thakur says:

2413 hrs

14. ZG Colorforce says:

One can use the method of finding total resistance in a parallel circiut too:
(1/a + 1/b)^(-1) = 2
(1/a + 1/c)^(-1) = 3
(1/a + 1/c)^(-1) = 4
(1/a + 1/b + 1/c)^(-1) = t
t = 24/13
Finding the total resistance in a parallel circuit and this is mathematicly the same question as this problem.

15. Spencer Chen says:

There’s possibility that someone is pulling back so that despite the fact 3 people work together but take longer time to done it

We learned to use (1/A + 1/B = 1/X) and (1/A + 1/C = 1/Y) and (1/B + 1/C = 1/Z) and solve for H in (1/A + 1/B + 1/C = 1/H) in mid. school (i think 6th grade) in Iran.

17. Alexandra Oporto says:

So the key to understand the problem is notice the relation of the hours and individual work with the constant rate, so proper equations could be formed.

18. Fran says:

19. Gaikokujohn says:

Bob and Charlie will dp Alice in 4.5 hours

20. Daily Dose Of Cubing says:

Here’s my take, Alice can complete her tasks in .5 hours, bob can complete in 1.5 hours, and Charlie in 2.5, it adds up to 4.5 hours

21. King Oblivion says:

Ayyyye I was right.

22. Hounten says:

I did this in my head and got 4.5 then reread the question and then contemplated my education

23. Christopher Perez says:

I knew it was percentage based but I didn’t know how to convert what I was thinking into a formula and I was always thing a bit wrong is saying that each person does a certain percentage of the job and that was a fixed number (like Alice always did 60% of the job or something)

24. Sanjay Kumar says:

No time is needed to complete the work because it has already been done in the first time only

25. Somebody Likes Bacon Games says:

Charlie, only saving 9 minutes of time. Classic Charlie.

26. Kim Delapena says:

(1/rA + 1/rB)= 1/2
(1/rA+1/rC) = 1/3
(1/rB+1/rC) =1/4
2*(1/rA+1/rB+1/rC)= 13/12
1/rA + 1/rB + 1/rC = 13/24 meaning that they accomplish about 54.17% of the work in 1 hr by working together so they can finish the work in 24/13 hrs

27. Katy Holiday says:

this seems like a typical gcse question in the uk

28. C4LIBR3S Dylan says:

Not a common answer but the job may be quick but they argue a lot.
Alice and bob could argue less than alice and charlie. And bob and charlie argue more than alice and bob do. Bob likes alice better than charlie. Charlie likes alice more than bob. They could just get along with each other and all do it together in an hour.

29. L Castillo says:

Tricky, tricky. Hahaha

30. Arnav Bagga says:

I did it in my head in 10 seconds. Oh wait I'm Indian..

31. The Amazing Channel says:

US people don't study anything
Bright students from other countries immigrate to US and make USA better

The more people you assign to a job the more it takes to get it done. It's just common sense 🙂

33. The Abominable Trollman says:

Isn't this the problem Minkus/Mincus got wrong?

34. Jordi Martinez says:

Conclusion Alice did the job, Bob was for moral support and Charlie….. well no comments 😂😂😂😂

35. Al Garnier says:

It will take 2 hours if Charlie is not allowed to interfere with the process!
Charlie must be a supervisor.

36. Nights Only says:

The only thing I could conclude is that someone needs make Charlie’s lazy ass do more work!!

37. ilia rasouli says:

Bruh we learn these types of questions in highschool.

38. deezynar says:

360 boxes need to be moved.
A+B MOVE 1/2 OF THEM / HOUR, OR 180 / HOUR
A+C MOVE 1/3 OF THEM / HOUR, OR 120 / HOUR
B+C MOVE 1/4 OF THEM / HOUR, OR 90 / HOUR
A MOVES 105 / HOUR, B MOVES 75 / HOUR, C MOVES 15
105 + 75 + 15 = 195 / HOUR
1.846 HOURS / 360 BOXES
1.846 HOUS = 1:51

39. eye gamer says:

I got 1 hour and 53 mins in my ans.

40. Dave Zimmerman says:

Great math but an employer will have Charlie fired or work by himself monitor productivity and fire him if needed
Do the cost analysis : Paying Charlie for two hrs only gets you 18 mins of productivity! hit the road Jack ! Throwing more people at some jobs makes it take longer and/or less productivity
fire the supervisor/ manager if it happens again
That’s the solution

41. Dave Zimmerman says:

Great math but an employer will have Charlie fired or work by himself monitor productivity and fire him if needed
Do the cost analysis : Paying Charlie for two hrs only gets you 18 mins of productivity! hit the road Jack ! Throwing more people at some jobs makes it take longer and/or less productivity
fire the supervisor/ manager if it happens again !
Another way to look at it is : if Charlie is their instead of bob he gives a half hearted effort so Alice doesn’t have to do all the work herself . But put Charlie with bob and he will let bob do all the work! Fire Charlie , That’s the solution

42. Elvis Pfützenreuter says:

It is a terribly ill-posed problem

43. andrew2343 says:

i ended up converting job to distance and the combinations of people into vehicles going at a certain speed. To make it ez, i made the distance 100km, so alice and bob are a vehicle going at 50km/h, alice and charlie one going at 33.33km/h and bob and charlie one going at 25. Then you make it so each individual person represents a certain ammount of speed, so sa + sb = 50km/h and so on. Then its just a simple equation system and dividing 100 by whatever speed you get for sa + sb + sc and then converting whatever you get to hours and minutes. This will give you the 1h 51 minutes travel time.

44. Suklesh Kumari says:

This is the first and easiest problem in 7th grade mathematics book in india and even college students can't solve it.
Shame

45. Goran Sekulic says:

a + b = 2 etc happens when you have a dysfunctional educational system. Ok, I haven't done any real maths in like 8 years, so nobody can fault me, but if people who ARE a part of that system have this exact same problem…time to change the system.

edit: my most common math question: Why is this important, where will I use it, seems useless.

46. Navneet Kumar says:

this can be solved by any 7th grade student in INDIA….there is dedicated chapter taught here named "TIME AND WORK"

47. André Blanchet says:

I've solved this very simply. Let:
w = work done
a = work rate Alice
b = work rate Bob
c = work rate Charlie
where work rate = work done per hour.
Problem's statement is: w = 2(a + b) = 3(a + c) = 4(b + c)
We're searching x such that w = x(a + b + c) => x = w / (a + b + c). We have:
2a + 2b = 3a + 3c => a – 2b + 3c = 0
2a + 2b = 4b + 4c => a – b – 2c = 0
3a + 3c = 4b + 4c => 3a – 4b – c = 0
Solving these equations we get: a = 7c, b = 5c
Thus a + b = 12c => a + b + c = 13c
Since w = 2(a + b) = 24c we get x = 24/13 hours.

48. Void says:

I thought in physic terms to solve it: time x (Velocity_A + Velocity_B + …) = distance (job)

49. Al Tinfoil says:

Presh' answer makes sense in his model world where every person works at a constant rate AND DOES NOT INTERFERE IN THE OTHERS' WORK. Both assumptions do not necessarily apply outside the mathematical model world. In the real world, a coworker may not only work slowly, but may interfere in the other's work by engaging the other in conversation, asking questions, making the other wait for the first to finish a stage before handing the work to the faster worker, checking his/her iphone for messages, texting, bathroom breaks, arguing about how the work should be done, criticizing the other's work product, sabotaging the other's work in order to look better to the boss, etc.

50. 治勋胡 says:

This can easily be solved by a primary school student in China….I could do this when I was 10.

51. Pokemon Master Zubi says:

In India we solve this problem in class 5 or 6

52. Xen8tor says:

This question was asked by our teacher in an exam in 10th class…and i solved it

53. NoName says:

I just made A + B = 1Job/ 2hour

54. BrokeAngler INC says:

am i tbe only one who finish a work faster alone than with buddies?
..u know…a drink or two in between, roasting each other,

55. Chloe Price says:

As a college student who has knowingly turned in incorrect answers, it's not that we don't think about whether the answer makes sense, it's that we don't know how to get the real answer and it's better to put something on the paper in the hopes of partial credit, even if it's wrong.

1hr 50.769secs.

57. ontarian says:

2x(1/(1/2+1/3+1/4))=24/13

58. Albert Einstein says:

I am in grade 7 and I did it the way the U.S. college students did it.

59. Nipun Jain says:

I approach these type of questions using velocity-displacement-time formula, i.e v=s/t. Where, v can be used as the rate at which a person does the work, s be the work and t be the time taken.
Here
Va+Vb=W/2
Va+Vc=W/3
Vb+Vc=W/4,
And
Va+Vb+Vc=W/t
t can easily be calculated by adding the first three eqns and dividing the eqn by 2 on both sides.

60. Aaron Justin says:

I am happy that I solved it.

61. Tapas Panda says:

A + B in one hour complete 1/2 job
B + C in one hour complete 1/3 job
C + A in one hour complete 1/4 job
So in one hour 2(A + B + C) complete 1/2 + 1/3 + 1/4 = 13/12 job
=> A + B + C in one hour complete 13/24 job
So to complete the job they need 24/13 hour.

62. Ali Sina says:

The real question is what were Alice and Charlie doing in that extra hour? Specifically, did they use a condom? And what beer joint did Bob and Charlie go to before they started work?

63. Martin Cattell says:

I got one hour and 27.5 minutes.
I reasoned that:
A + B complete 1/2 a job in 1 hour
A + C complete a 1/3 in 1 hour
B + C complete 1/4 in 1 hour

If duplicate people were possible:
(A + B) + (A + C) + (B + C) = 2(A + B + C) would complete 13/12 job in one hour
meaning A + B + C would complete 13/24 job in one hour.
To complete the remaining 11/24, 11/24 * 1 hour would be needed or 27.5 minutes.

EDIT: Derp!
If 13/24 of the job is completed in 1 hour then it takes 11/13 hours to complete the remaining 11/24 of the job which is 51 minutes. I should have never doubted you!

64. Ayder Al says:

Too complicated for non-matematicians. Use W=V*T i.e. work = speed * time instead of (percentage per time) * (time). For many people speed is more natural term.
A + B = 1/2 has meaning that speed of Alice and Bob equals to half job per hour and etc.

65. Suyash 11 says:

If my friend does his work in 2 hours and I do the same work in 1 hour that doesn't mean that we both combined can do it in a specific time limit. We can finish it in 0.5 hours also if we are determined and work together with coordination and we can finish it in 4 hours also if we don't do it with proper teamwork and determination. So, the question is pointless. You can't predict anything. Questions asking that if a car travels at 50 kmph stops after 10 hours how much distance would it have covered are pointless too coz it's not necessary that motion is uniform and even if it is, it's unpredictable until many conditions are specified. We just think of everything as ideal and therefore the questions which we solve can't be applied on real situations. Like , neglecting Air resistance would not work in freely falling body questions.

66. chuggle gluggle says:

I got it immediately. College students must be a little slow

67. Peter Roelofsen says:

Law of diminishing returns in economics, one of the few practical things I learned at school in Economics classes that I still remember.

68. Mark Levin says:

There will be lots more talking yelling argueing. Therefore i would take a lot longer….

69. sha vi says:

I do with same equation thank you

70. Sacheta Bhardwaj says:

I did it correct

71. Douglas Brinkman says:

so Charlie isn't much help.

72. Suvinay Goyal says:

its quite easy, easier than what u have done
work done by a+b in 1 hour = 1/2
work done by a+c in 1 hour = 1/3
work done by b+c in 1 hour = 1/4
work done by a+b+a+c+b+c in 1 hour = 1/2+1/3+1/4 => 2(a+b+c)= 13/12
work done by a+b+c in 1 hour = 13/24
total time for them to do the work= 24/13= 1 hour 51 mins

73. Anand Patel says:

I did 6/9

74. Kamala Kanta Mishra says:

A SSC aspirant in India can solve this problem in 15-20 seconds

75. Ya Boi Danny says:

A=.5 hours
B=1.5 hours
C=2.5 hours
A+B+C=4.5 hours

See? It IS a valid answer!

76. silverfeathered1 says:

I think "basic" is the wrong choice of words. "Common" fits much better.

In management, this sort of math is routine. We'd assign manpower value to each employee to make sure we have enough to do the task. On smaller scales, most small businesses estimate this type of math intuitively.

If we think of Alice as the veteran employee, Bob the average employee, and Charlie the new hire; we assign an estimated manpower value to each with Bob as the value of 1.
Alice would receive a higher value due to her proficiency.
Charlie would be a fractional in the above example to keep the math simple. Although, typically I'd assign a negative value due to trainees pulling manpower to be taught.

77. seathom play says:

If Alice, Bob and Charlie are getting paid for this work, I'd say fire Charlie, he only helps to get the job done 9 minutes faster than if Alice and Bob worked alone! What a slacker.

78. Steve Zelaznik says:

They need to make it clear that this task can be completed in parallel, for example painting a room or shoveling a sidewalk.

79. Johnny Facchin says:

I did it my head and it took me like a minute but I came up with 1 hour and 50 minutes…close

80. Priyam Dey says:

Why is this Question considered hard
We used to solve same type of Q in class 7 and we could figure it out even at that time

81. Nascha Lecter says:

What? It's just simultaneous equation. Plus, is working with more people for one chore can make it done faster?

82. ken kennedy says:

This is a trick question. Every manager knows that it will take as many hours as there are left in the day.

83. Rohan Gupta says:

me : *solves the problem by looking at the thumbnail in my mind *
me : Where is my medal ?

84. The Next says:

I m not a college student. But I made the same mistake 🤨

85. Bhupinder Kaurhut says:

“Too many cooks spoil the broth”
So more people completing the job in more time can be true in some cases.

86. Markandey Kumar says:

Here is the more easier method ☺️
Let's suppose 'T' time taken by all to complete work when working together.
Then part of work done by (A+B) = T/2 ……..eqn(1)
Similarly part of work done by (A+C) = T/3……. eqn(2)
AND
Part of work done by pair (B+C) = T/4…….(eqn)
Since once we add above parts of work we get twice of work done because
(A+B)+(A+C)+(C+B)=2(A+B+C)
So on adding parts of work done by individual pairs in T time we got following equation
(T/2) + (T/3) + (T/4) = 2
T × (13/12) = 2
T = 2×12/13
T = 24/13
T = 1Hour 51 min.
Where A: Alice ; B: Bob ; C: Charlie

87. Vimlesh Maheshwari says:

Very easy question

88. VEVO LK says:

We can think this problem in another corner. Like Take the work as distance , and the
2(speed of A + speed of B) = S
3(speed of A + speed of C) = S
4(speed of B + Speed of C) = S.
By solving this we can get the answer. This is my method. It actually looks like your method.
Actually I Really proud of my self.
🇱🇰 I'm a Sri lankan.

89. Goku Black . says:

I can't believe they failed to solve this

90. Bailey Harrison says:

I think an easier way to work this out is set out the equations as:
a+b=1/2
a+c=1/3
b+c=1/4
And then the answer is the reciprocal of a+b+c

91. Shxdow Tsxrdom says:

I mean, i just did trial and error to sum it all up, figured bob would be 1.30 and alice .30, so 4 – 1.30 =2.30, so .30+1.30+2.30 = 4.30

Yes .30 as in half of an hour

92. koon wong says:

The answer is infinity. everyone was waiting for the other two to do the job, so nobody did it.

93. FiNNiK says:

I think that's why physics is so helpful when facing math problems.
This was basically a no-brainer if you understand how speed and time for example are connected.

94. patrickk says:

Guess it was sort of incorrect You can immidiately see 3 names begining with letters a b and c. Having 3 formulas means we can solve for all three of them

95. Gaurav Muthusamy says:

Let’s make the amount of a job Alice can do in an hour be A, and B for Bob and C for Charlie. Then we take A+B, which is the sum of his much Alice and Bob can do in an hour. If they do 1 job in 2 hrs, they do 1/2 job in 1 hr. So A+B=1/2. So for A+C, since they do it in 3 hrs, they do 1/3 job in an hr. A+C=1/3. Then obviously B+C=1/4, applying the same rule. So A+B-1/6=A+C, B-1/6=C. Now we have B+C=1/4, B+B-1/6=1/4, 2B=5/12, B=5/24. So C=5/24-1/6=1/24. So A+1/24=1/3, A=7/24. So we have A+B+C=7/24+5/24+1/24=13/24 of a job per hr. So to find hrs for one job, we do (13/24)/1=1/x, cross-multiply to get (13/24)x=1, x *24/13 hrs*. Boom. How do college kids get this wrong, I got this in less than 3 minutes and I’m a sophomore in high school. Also Bruh Charlie sucks ass

96. Artemirr Lazaris says:

🙁 I wasl ike the answer doesn't make sense… then I was like.. I need ot know J.. and find out T and it has to be less than 2 hours. I mean I would of guessed one hour… but I set it up the wrong way… It knowing what you can do toa question that reveals it. I didn't know I could assign 1 as 100% for J. Which would of led me down the correct path… the notion of thoguth stating.. hey. 2A+2B=1 one representing the missing theing for meaning 100% of the job takes. Thus equal to one… A B are going ot be a varrible or fraction/ percentage of it. Hwoever you wish to word it. Logic states to me that A works the fastest, B mid, nad C slowest.. so I was doing other nonsense maths, lol.. but.. if you don't know something then work with what is given. So regardless fo who works faster, simply put that both take 2 hours to complete the job, and the variable is there somewhere… there first method works if YOU know how long the Job takes and thus you should subjtract from the job… So I had something like A + B – J = 2 hours. lol.. That wasn't getting me anywhere.. lol…

97. jcb3393 says:

Hooray! I got it (because I caught the trick: it's about rates, i.e., quotients). Therefore, it's about a harmonic mean, not a geometric or arithmetic mean.

98. Deepak Raja Murugesan says:

I solved it myself in right way by my first step😉

99. kartheek pawar says: