Pipes A and B can fill an entire tank in 8 hours and 12 hours, respectively. The water tank is one-fourth full. If both the pipes are opened together, then how long will it take to fill the remaining part of the tank?
3 hours 36 minutes
Pipe A fills the tank in 8 hours, so in one hour it fills \(\frac{1}{8}\) of it; pipe B fills it in 12 hours, filling \(\frac{1}{12}\) per hour.
Opened together, their combined rate is \(\frac{1}{8}+\frac{1}{12}=\frac{3+2}{24}=\frac{5}{24}\) of the tank per hour.
The tank is already one-fourth full, so the part still to be filled is \(1-\frac{1}{4}=\frac{3}{4}\).
Time = work ÷ rate = \(\frac{3}{4}\div\frac{5}{24}=\frac{3}{4}\times\frac{24}{5}=\frac{18}{5}\) hours.
Now \(\frac{18}{5}=3.6\) hours, and 0.6 hour = 36 minutes.
Hence, the answer is 3 hours 36 minutes.
Similar Questions
Three pipes A, B and C can fill a tank in 12 hours, 18 hours and 24 hours, respectively. A leak at the bottom can empty the full tank in 36 hours. If all the pipes are opened together, in how many hours will the tank be filled? (Round off your answer to two decimal places.)
A pump can fill a tank in 3 hours. Due to a leak in the tank, it takes 4.5 hours to fill the
tank. In how much time can the leak empty the full tank if no other entry or exit routes
are open?
Important Questions from Pipe and Cistern
Pipes A, B and C can fill a tank in 20, 30 and 60 hours, respectively. Pipes A, B and C are opened at 7 a.m., 8 a.m., and 9 a.m., respectively, on the same day. When will the tank be full?
There are two water taps in a tank which can fill the empty tank in 12 hours and 18 hours respectively. It is seen that there is a leakage point at the bottom of the tank which can empty the completely filled tank in 36 hours. If both the water taps are opened at the same time to fill the empty tank and leakage point was repaired after 1 hour, then in how much time the empty tank will be completely filled?
Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All the three pipes are opened simultaneously. However, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
Pipes A and B can fill a tank in 12 hours and 16 hours respectively and pipe C can empty the full tank in 24 hours. All three pipes are opened together, but after 4 hours pipe B is closed. In how many hours, the empty tank will be completely filled?
Pipes A and B can fill a tank in 43.2 minutes and 108 minutes, respectively. Pipe C can empty it at 3 litres/minute. When all the three pipes are opened together, they fill the tank in 54 minutes. The capacity (in litres) of the tank is:
