Two pipes can fill a tank in 12 hours and 15 hours respectively, and a third pipe can empty it in 6 hours. Starting with the tank empty, the first two pipes are kept open for 5 hours, and then the third pipe is also opened. After all three pipes are open, how long does it take for the tank to become empty?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 45 hours
A filling pipe adds its part of the tank every hour and an emptying pipe takes its part away. With all three open, the net rate decides whether the tank fills or empties.
Filling in one hour by the first two pipes \(\displaystyle =\frac{1}{12}+\frac{1}{15}=\frac{5+4}{60}=\frac{3}{20}\) of the tank
Water in the tank after 5 hours \(\displaystyle =5\times\frac{3}{20}=\frac{3}{4}\) of the tank
Net change per hour with all three open \(\displaystyle =\frac{3}{20}-\frac{1}{6}=\frac{9-10}{60}=-\frac{1}{60}\), so the tank loses \(\frac{1}{60}\) of its volume every hour
Time to empty \(\frac{3}{4}\) of the tank \(\displaystyle =\frac{3}{4}\div\frac{1}{60}=45\) hours
The tank becomes empty 45 hours after the third pipe is opened.