A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 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 10 hours and emptied by another pipe in 5 hours. If both pipes are opened together, how long will it take to fill the tank?
10 hours
5 hours
15 hours
20 hours
The net rate is 1/10 - 1/5 = -1/10. Therefore, the tank will never fill.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/10 - 1/5 = -1/10. Therefore, the tank will never fill.
Steps: 8
Step 1: Understand that one pipe fills the tank and the other pipe empties it.
Step 2: Determine the filling rate of the filling pipe. It fills the tank in 10 hours, so its rate is 1/10 of the tank per hour.
Step 3: Determine the emptying rate of the emptying pipe. It empties the tank in 5 hours, so its rate is 1/5 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: (1/10) - (1/5).
Step 5: Convert 1/5 to a fraction with a denominator of 10: 1/5 = 2/10.
Step 6: Now, calculate the net rate: (1/10) - (2/10) = -1/10.
Step 7: The negative net rate (-1/10) means that the tank is being emptied faster than it is being filled.
Step 8: Conclude that if both pipes are opened together, the tank will never fill.
