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
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):
| Rate (tub/min) | Time (min) | Work (tubs) | |||
| P | 1/10 | × | 6 | = | 3/5 |
| Q | 1/(t – 4) | × | 6 | = | 6/(t – 4) |
| Drain | –1/t | × | 6 | = | –6/t |
| Total | n/a | n/a | 1 |
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.
