A tank can be filled by a pipe in 15 hours and emptied by another pipe in 10 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 15 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
30 hours
20 hours
25 hours
15 hours
The net rate is 1/15 - 1/10 = -1/30. Therefore, the tank will never fill.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank can be filled by a pipe in 15 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/15 - 1/10 = -1/30. Therefore, the tank will never fill.
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 15 hours, so its rate is 1/15 of the tank per hour.
Step 3: Determine the rate at which the emptying pipe works. It empties the tank in 10 hours, so its rate is 1/10 of the tank per hour.
Step 4: Calculate the net rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/15) - (1/10).
Step 5: Find a common denominator to perform the subtraction. The common denominator for 15 and 10 is 30.
Step 6: Convert the rates: (1/15) = 2/30 and (1/10) = 3/30.
Step 7: Now subtract the rates: (2/30) - (3/30) = -1/30.
Step 8: The negative result (-1/30) means that the tank is being emptied faster than it is being filled.
Step 9: Conclude that if both pipes are opened together, the tank will never fill.
