An inlet pipe can fill an empty tank in 9 hours. The tank is empty and only this pipe is opened. When the tank is half full, a leak develops at its bottom, and the pipe then takes 6 more hours to fill the tank completely. In how many hours can the leak alone empty the full tank?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 36 hours
The leak acts only on the second half of the filling. That half took 6 hours, which gives the net rate with the leak; the leak's rate is the pipe's rate minus this net rate.
Net rate with the leak \(\displaystyle =\frac{1}{2}\div6=\frac{1}{12}\) of the tank per hour
Pipe alone fills \(\frac{1}{9}\) of the tank per hour
Leak empties \(\displaystyle \frac{1}{9}-\frac{1}{12}=\frac{4-3}{36}=\frac{1}{36}\) of the tank per hour
The leak alone empties the full tank in 36 hours.