Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both pipes are opened together, how long will it take to fill the tank?
Practice Questions
1 question
Q1
Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both pipes are opened together, how long will it take to fill the tank?
2 hours
3 hours
4 hours
5 hours
The net rate is 1/6 - 1/4 = -1/12. Therefore, the tank will never fill.
Questions & Step-by-step Solutions
1 item
Q
Q: Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/6 - 1/4 = -1/12. Therefore, the tank will never fill.
Steps: 8
Step 1: Determine the rate at which Pipe A fills the tank. Pipe A can fill the tank in 6 hours, so its rate is 1 tank per 6 hours, or 1/6 of the tank per hour.
Step 2: Determine the rate at which Pipe B empties the tank. Pipe B can empty the tank in 4 hours, so its rate is 1 tank per 4 hours, or 1/4 of the tank per hour.
Step 3: Calculate the net rate when both pipes are opened together. Since Pipe A fills and Pipe B empties, we subtract Pipe B's rate from Pipe A's rate: 1/6 - 1/4.
Step 4: To subtract the fractions, find a common denominator. The common denominator for 6 and 4 is 12.
Step 5: Convert the rates to have the common denominator: 1/6 = 2/12 and 1/4 = 3/12.
Step 6: Now subtract the rates: 2/12 - 3/12 = -1/12.
Step 7: The negative result (-1/12) means that when both pipes are opened together, the tank is actually being emptied at a rate of 1/12 of the tank per hour.
Step 8: Since the net rate is negative, the tank will never fill up when both pipes are open.
