Solving Pipe Filling and Emptying Problems
This problem involves calculating the time taken to fill a tank when one pipe fills it and another empties it simultaneously.
Calculating Filling Pipe Rate
The first pipe fills the tank in 5 hours. Its filling rate is the amount of the tank it fills per hour.
- Rate of filling pipe = \(\frac{1}{5}\) tank per hour.
Calculating Emptying Pipe Rate
The second pipe empties the tank in 10 hours. Its emptying rate is the amount of the tank it empties per hour.
- Rate of emptying pipe = \(\frac{1}{10}\) tank per hour.
Combined Work Rate
When both pipes work together, the net rate at which the tank fills is the filling rate minus the emptying rate.
- Net filling rate = (Rate of filling pipe) - (Rate of emptying pipe)
- Net filling rate = \(\frac{1}{5} - \frac{1}{10}\)
- To subtract, find a common denominator, which is 10:
- Net filling rate = \(\frac{2}{10} - \frac{1}{10} = \frac{1}{10}\) tank per hour.
This means that when both pipes are open, \(\frac{1}{10}\) of the tank is filled every hour.
Total Time Calculation
To find the total time required to fill the tank, divide the total work (filling 1 tank) by the net filling rate.
- Time = \(\frac{\text{Total Work}}{\text{Net Filling Rate}}\)
- Time = \(\frac{1 \text{ tank}}{\frac{1}{10} \text{ tank per hour}}\)
- Time = \(1 \times \frac{10}{1}\) hours
- Time = 10 hours.
Therefore, it will take 10 hours for both pipes to fill the tank when working together.
Similar Questions
- Three pipes of diameters 2 cm, 3 cm and 4 cm are running together to fill a cistern. The smallest pipe alone can fill the cistern in 232 minutes. The amount of water flowing in each pipe is proportional to the square of its diameter. The time (in minutes) taken by all pipes running together to completely fill the cistern is:
- A pipe can fill a sump with water in 2 hours. Because of a leak, it took $2 \frac{1}{3}$ hours to fill the sump. The leak can drain all the water of the sump in:
- Two pipes A and B can fill an empty cistern in 18 and 27 hours, respectively. Pipe C can drain the entire cistern in 45 hours when no other pipe is in operation. Initially, when the cistern was empty Pipe A and Pipe C were turned on. After a few hours Pipe A was turned off and Pipe B was turned on instantly. In all, it took 55 hours to fill the cistern. For how many hours was Pipe B turned on?
- Pipes A, B and C are attached to an empty cistern. While the first two can fill the cistern in 4 and 10 hours, respectively, the third can drain the cistern, when filled, in 6 hours. If all the three pipes are opened simultaneously when the cistern is half-full, how many hours will be needed to fill the cistern?
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?
