Manhattan GMAT Challenge Problem of the Week – 16 Nov 2010
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Question
A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?(A) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Answer
Let t stand for the desired time, so that the drain can empty the tub in t minutes and faucet Q can fill the tub in (t 4) minutes.Also, the drain does negative work as it empties the tub.The rates for the pipes and the drain are thus
P: 
Q: 
Drain: 
Using the fact that all three fixtures together take 6 minutes to fill 1 tub, set up an RTW chart, and use the chart to calculate the total work quantities (shown in boldface):
Set up an equation:
Multiply by the common denominator, 5t(t 4):
t = 10 OR t = 6
The negative value is absurd, so t = 10; the drain can empty the tub in 10 minutes.
The correct answer is C.
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