A pipe can fill an overhead tank in 12 hours. But due to a leak at the bottom,…
2024
A pipe can fill an overhead tank in 12 hours. But due to a leak at the bottom, it is filled in 18 hours. If the tank is full, how much time will the leak take to empty it?
- A.
3.6 hours
- B.
63 hours
- C.
7.2 hours
- D.
36 hours
Attempted by 7 students.
Show answer & explanation
Correct answer: D
Rate of the pipe: The pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour.
Net rate with leak: Because of the leak, it takes 18 hours to fill, meaning the net filling rate is 1/18 of the tank per hour.
Determine the leak rate: The net rate is the pipe's rate minus the leak's rate.
(Pipe Rate) - (Leak Rate) = (Net Rate)
(1/12) - (Leak Rate) = (1/18)
Leak Rate = (1/12) - (1/18)
Using a common denominator of 36: (3/36) - (2/36) = 1/36 of the tank per hour.
Time to empty: Since the leak empties the tank at a rate of 1/36 per hour, it will take 36 hours to empty the full tank.