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Work rate problem

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by ysfpsu » Mon Mar 14, 2011 6:02 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 GMATGuruNY » Mon Mar 14, 2011 6:22 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!
Plug in a value for the pond.

Let pond = 6 liters.
Pump A takes 3 hours to empty half the pond, so the time for Pump A to empty the whole pond is 6 hours.
Rate for Pump A = w/t = 6/6 = 1 liter per hour.
Pumps A and B together take 1/2 hour to empty half the pond, so the time for Pumps A and B together to empty the whole pond is 1 hour.
Combined rate for Pumps A and B = w/t = 6/1 = 6 liters per hour.
Thus, rate for Pump B alone = Combined rate - Rate for A alone = 6-1 = 5 liters per hour.
Time for Pump B alone to empty the pond = w/r = 6/5 = 1.2 hours.
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by ysfpsu » Mon Mar 14, 2011 6:30 pm
Thank you so much. Very straightforward. My issue was that I was reading too much into the question. I was trying to figure out how long it would take Pump B to just do its part for the half of the pond remaining without plugging in a value for the whole pond. Got lost in the calculations.
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