A tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours
Practice Questions
Q1
A tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours. If both pipes are opened together, how long will it take to fill the tank?
3.6 hours
4 hours
5 hours
6 hours
Questions & Step-by-Step Solutions
A tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 18 hours
Step 1: Understand that one pipe fills the tank in 6 hours. This means it fills 1/6 of the tank in one hour.
Step 2: Understand that the other pipe empties the tank in 9 hours. This means it empties 1/9 of the tank in one hour.
Step 3: Calculate the net effect when both pipes are open. The filling pipe adds 1/6 of the tank, and the emptying pipe removes 1/9 of the tank.
Step 4: To find the net rate, subtract the emptying rate from the filling rate: 1/6 - 1/9.
Step 5: To perform the subtraction, find a common denominator for 6 and 9, which is 18.
Step 6: Convert 1/6 to 3/18 and 1/9 to 2/18.
Step 7: Now subtract: 3/18 - 2/18 = 1/18.
Step 8: The net rate of filling the tank is 1/18 of the tank per hour.
Step 9: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 divided by 1/18 equals 18 hours.
Rate of Work – Understanding how to calculate the rate at which a tank is filled or emptied by different pipes.
Combined Work Rate – Calculating the net effect of multiple processes working together, such as filling and emptying a tank.
