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?
Practice Questions
1 question
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
The net rate is 1/6 - 1/9 = 1/18. Therefore, it will take 18 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: The net rate is 1/6 - 1/9 = 1/18. Therefore, it will take 18 hours to fill the tank.
Steps: 9
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.
