A tank can be filled by a pipe in 9 hours and emptied by another pipe in 18 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 9 hours and emptied by another pipe in 18 hours. If both pipes are opened together, how long will it take to fill the tank?
6 hours
9 hours
12 hours
15 hours
The net rate is 1/9 - 1/18 = 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 9 hours and emptied by another pipe in 18 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/9 - 1/18 = 1/18. Therefore, it will take 18 hours to fill the tank.
Steps: 9
Step 1: Understand that one pipe fills the tank and the other pipe empties it.
Step 2: Determine the rate at which the filling pipe works. It fills the tank in 9 hours, so its rate is 1 tank per 9 hours, or 1/9 of the tank per hour.
Step 3: Determine the rate at which the emptying pipe works. It empties the tank in 18 hours, so its rate is 1 tank per 18 hours, or 1/18 of the tank per hour.
Step 4: Calculate the net rate when both pipes are open. This is done by subtracting the emptying rate from the filling rate: (1/9) - (1/18).
Step 5: To subtract these fractions, find a common denominator. The common denominator for 9 and 18 is 18.
Step 6: Convert 1/9 to have a denominator of 18: (1/9) = (2/18).
Step 7: Now subtract: (2/18) - (1/18) = (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 / (1/18) = 18 hours.
