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.
Similar Questions
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?
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?
Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?
Two valves A and B can fill a sump in \(37\frac{1}{2}\) minutes and 45 minutes respectively. Both valves are opened. The sump will be filled in just 30 minutes, if valve B is turned off after?
One pipe can fill an empty cistern in 4 hours while another can drain the cistern when full in 10 hours. Both the pipes were turned on when the cistern was half-empty. How long will it take the cistern to be full?
A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twelfth of its capacity, during the second hour at one-ninth of its capacity, during the third hour at one-sixth of its usual capacity, during the fourth hour at one- fourth of its usual capacity and during the fifth hour it was only one-third as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank at a constant rate, the empty cistern could be filled in 5 hours, all the three pipes working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?
Pipes A and C can fill an empty cistern in 16 and 24 hours respectively while Pipe B can drain the filled cistern in 12 hours. If the three pipes are turned on together when the cistern is empty, how many hours will it take for the cistern to be full?
Pipes A and C can fill an empty cistern in 32 and 48 hours, respectively while pipe B can drain the filled cistern in 24 hours. If the three pipes are turned on together when the cistern is empty, how many hours will it take for the cistern to be 2/3 full?
One of the two inlet pipes works twice as efficiently as the other. The two, working alongside a drain pipe that can empty a cistern all by itself in 8 hours, can fill the empty cistern in 8 hours. How many hours will the less efficient inlet pipe take to fill the empty cistern by itself?
- Two pipes fill a tank when working individually in 25 and 40 hours, respectively while a third pipe can drain the filled tank in 16 hours. If all the three pipes are turned on at the same time when the tank is empty, how long will it take to fill the tank completely?
Important Questions from Pipe and Cistern
A pipe can fill a cistern in 20 minutes where as the cistern when full can be emptied by a leak in 28 minutes. When both are opened, The time taken to fill the cistern is:
‘A’ pipe can empty a tank in 20 minutes. The second pipe ‘B’ has a diameter twice as that of ‘A’. If both A & B pipe are attached to the tank how much time will be required to empty the tank?
Pipes A and B can empty a full tank in 16 hours and 24 hours, respectively. Pipe C alone can fill the empty tank in 4 hours. If A, B and C are opened together, the tank will be 35% full after :
Pipes A and B can fill a tank in 36 minutes and 45 minutes, respectively. Both these pipes were opened simultaneously. After 20 minutes, a leak at the bottom of the tank was spotted which was immediately sealed. The tank was full in another 15 minutes. The leak alone can empty the full tank in:
A cistern has a leak which would empty it in 6 hours. A tap is turned on which admits 10 litres of water per minute into the cistern. When it is full it is now emptied in 10 hours. What is the capacity (in litres) of the cistern?
