Yesterday Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the 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
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,
The negative value is absurd, so t = 10; the drain can empty the tub in 10 minutes.
The correct answer is C.