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Work rate problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Work rate problem

by ysfpsu » Mon Mar 14, 2011 5:41 pm
Okay I feel stupid posting this question because it seems really easy but I, for the life of me, can't figure it out...(doesn't bode well for my Quant section..)

One pump drains one-half of a pond in 3 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?

Answer is: 1.2 hours

I know you have to find the rate of pump A (1/6), find the rate of Pump A and B together ( 1hr). Subtract to get rate of Pump B then using W = rt, find the time. But I can't get the answer!! Please help!
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by Geva@EconomistGMAT » Mon Mar 14, 2011 11:50 pm
ysfpsu wrote:Okay I feel stupid posting this question because it seems really easy but I, for the life of me, can't figure it out...(doesn't bode well for my Quant section..)

One pump drains one-half of a pond in 3 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?

Answer is: 1.2 hours

I know you have to find the rate of pump A (1/6), find the rate of Pump A and B together ( 1hr). Subtract to get rate of Pump B then using W = rt, find the time. But I can't get the answer!! Please help!
deal with this sort of problem by plugging in a comfortable number for the work. You want a number that is easily divisible by 2 (one half of a pond), and by three (3 hours) so that you avoid fractions. So assume that the pond is 6 liters.

The first pump drains one half of the pond (3 liters) in 3 hours, or a rate of 1 liter an hour.
The second pump kicks in, and the two pumps together drain the pool (the remaining 3 liters) in half an hour: meaning that they work at a rate of 3/1/2 = 3*2 = 6 liters an hour together.

since the combined rate is 6 li/h but the first pump's rate is 1 liter/hr, the second pump's rate is the remaining 5 liters an hour. If the pump had to drain the entire pool (6 liters) at 5 lt/hr, it would take it 6/5 = 1.2 hours to do so.
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by gmatscottsdale » Mon Mar 21, 2011 2:30 am
Another way to approach this problem would be:

We know time taken by Machine A and Machine B to work together and finish the job is:

T = AB/(A + B)

In this case, the first pump finished draining half the pond in 3 hrs. To finish draining the full pond, it would take 6 hrs.

Similarly, when both machines started working together to rest the second half of the pond, they finished the job in 0.5 hrs. If they started working together right from the beginning, they would have drained the entire pond in 1 hr.

(I basically made sure I calculate the number of hours to drain the entire pond since the answer is asking how long will it take to drain the entire pond by using the second pump independently).


We plug our values, A = 6, B = unknown (x), and T = 1

6*x/(6 + x) = 1

=> 6x = (6 + x)

=> 6x - x = 6

=> 5x = 6

x = 6/5 = 1.2 hrs

:)
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by gmatscottsdale » Mon Mar 21, 2011 2:33 am
In reference to the point where you got stuck on this particular problem:

You are not getting the correct answer in the pump problem because you are probably forgetting to flip your answer.

You are right, you subtract:

Rate B = Rate(Combined) - RateA = 1 - 1/6 = 5/6

However, remember that Rate B = Work done/time, We know Work done is 1 and time = x

5/6 = 1/x => x = 6/5 = 1.2 hrs :)
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