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.)
6.55 hours
To find out how long it will take to fill the tank with all the pipes and the leak working together, we need to determine the net rate at which the tank fills. Let's calculate this step by step:
- The rate at which pipe A fills the tank is \( \frac{1}{12} \) of the tank per hour because it can fill the entire tank in 12 hours.
- Similarly, the rate at which pipe B fills the tank is \( \frac{1}{18} \) of the tank per hour.
- And pipe C fills the tank at a rate of \( \frac{1}{24} \) of the tank per hour.
- The leak, which empties the tank, works at a rate of \( \frac{1}{36} \) of the tank per hour.
- To find the net rate of filling the tank, we add the rates of pipes A, B, and C and subtract the rate at which the leak empties the tank. The equation is given by: \(\text{Net rate} = \left(\frac{1}{12} + \frac{1}{18} + \frac{1}{24}\right) - \frac{1}{36}\)
- Calculating each part:
- \( \frac{1}{12} = 0.0833 \) (approx.)
- \( \frac{1}{18} = 0.0556 \) (approx.)
- \( \frac{1}{24} = 0.0417 \) (approx.)
- \( \frac{1}{36} = 0.0278 \) (approx.)
- Add these rates: \(0.0833 + 0.0556 + 0.0417 - 0.0278 = 0.1528\)
- Therefore, the net rate at which the tank is filled is \( 0.1528 \) of the tank per hour.
- To find the total time required to fill one tank, we calculate the reciprocal of the net rate: \(\text{Time} = \frac{1}{0.1528} \approx 6.55 \text{ hours}\)
Hence, the time taken to fill the tank with all the pipes working along with the leak is approximately 6.55 hours. Therefore, the correct answer is 6.55 hours.
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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?
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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:
