Tank Fill Time Calculation with Multiple Taps
This problem requires calculating the total time to fill a tank when multiple taps, some filling and some emptying, operate simultaneously.
Tap Rates Explained
We first determine the rate at which each tap works, expressed as the fraction of the tank filled or emptied per hour:
- Tap A fills the tank in 6 hours. Its filling rate is $1/6$ tank per hour.
- Tap B fills the tank in 8 hours. Its filling rate is $1/8$ tank per hour.
- Tap C empties the tank in 4 hours. Its emptying rate is $1/4$ tank per hour. This contributes negatively to filling.
Combined Rate Calculation
When all taps are open together, the net rate of filling is the sum of the filling rates minus the emptying rate.
Combined Rate = (Rate of Tap A) + (Rate of Tap B) - (Rate of Tap C)
Combined Rate = $1/6 + 1/8 - 1/4$ tank per hour.
To combine these fractions, we find the Least Common Multiple (LCM) of the denominators (6, 8, 4), which is 24.
Combined Rate = $4/24 + 3/24 - 6/24$
Combined Rate = $(4 + 3 - 6) / 24$
Combined Rate = $1/24$ tank per hour.
Time Calculation
The time needed to fill the entire tank (1 whole tank) is the reciprocal of the combined filling rate.
Time = $1 / (\text{Combined Rate})$
Time = $1 / (1/24)$ hours
Time = $24$ hours.
Similar Questions
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- Two pipes can fill a cistern, individually, in 36 min and 45 min, respectively. There is a pipe located at the bottom of the cistern to empty it. If all the three pipes are opened simultaneously, then the empty cistern gets filled in 70 min. How long will the pipe at the bottom of the tank take to empty the completely filled cistern if no other pipe is then open?
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- Pipes A and B are fitted to a tank. A is the filling pipe and B can be used for filling or emptying at the same rate. When B is used for filling, it takes time 't' along with A to fill the tank. If it is used for emptying when A is filling the tank, the time taken for the tank to fill up would be '5t'. Find the ratio of the rates of A and B.
- 28 pipes are connected to a tank. Some of them pour water into the tank, whereas the rest drain water out of it. Each of the pipes that fill water can fill the empty tank in 14 hours, whereas any of the drainpipes can empty the filled tank in 35 hours. If all the pipes are opened simultaneously when the tank is empty and the tank is filled in 2.5 hours, how many of the pipes were drainpipes?
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:
