A tank has two pipes. Pipe A can fill the tank in 8 hours, and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
Practice Questions
1 question
Q1
A tank has two pipes. Pipe A can fill the tank in 8 hours, and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
4 hours
6 hours
8 hours
10 hours
The net rate is 1/8 - 1/12 = 1/24. Therefore, it will take 24 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank has two pipes. Pipe A can fill the tank in 8 hours, and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/8 - 1/12 = 1/24. Therefore, it will take 24 hours to fill the tank.
Steps: 7
Step 1: Determine the rate at which Pipe A fills the tank. Since Pipe A can fill the tank in 8 hours, its rate is 1 tank per 8 hours, or 1/8 of the tank per hour.
Step 2: Determine the rate at which Pipe B empties the tank. Since Pipe B can empty the tank in 12 hours, its rate is 1 tank per 12 hours, or 1/12 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 of Pipe B from the filling rate of Pipe A: (1/8) - (1/12).
Step 4: To subtract the fractions, find a common denominator. The least common multiple of 8 and 12 is 24.
Step 5: Convert the rates to have the same denominator: (1/8) = (3/24) and (1/12) = (2/24).
Step 6: Now subtract the two rates: (3/24) - (2/24) = (1/24). This means that together, both pipes fill 1/24 of the tank in one hour.
Step 7: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 divided by (1/24) equals 24 hours.
