A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 hours. If both pipes are opened together, how long will it take to fill the tank?
Practice Questions
1 question
Q1
A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 hours. If both pipes are opened together, how long will it take to fill the tank?
4 hours
5 hours
6 hours
7 hours
The net rate is 1/12 - 1/8 = 1/24. Therefore, it will take 24 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/12 - 1/8 = 1/24. Therefore, it will take 24 hours to fill the tank.
Steps: 7
Step 1: Determine the rate at which the filling pipe works. It can fill the tank in 12 hours, so its rate is 1 tank per 12 hours, or 1/12 of the tank per hour.
Step 2: Determine the rate at which the emptying pipe works. It can empty the tank in 8 hours, so its rate is 1 tank per 8 hours, or 1/8 of the tank per hour.
Step 3: Calculate the net rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/12) - (1/8).
Step 4: To subtract these fractions, find a common denominator. The least common multiple of 12 and 8 is 24.
Step 5: Convert the rates to have the common denominator: (1/12) = 2/24 and (1/8) = 3/24.
Step 6: Now subtract the two rates: (2/24) - (3/24) = -1/24. This means the tank is being emptied at a rate of 1/24 of the tank per hour.
Step 7: Since the net rate is negative, it indicates that the tank is emptying rather than filling. Therefore, it will never fill up if both pipes are open.
