A tank has two pipes. Pipe A can fill the tank in 8 hours, and pipe B can empty
Practice Questions
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
Questions & Step-by-Step Solutions
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?
Correct Answer: 24 hours
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.
Rate of Work – Understanding how to calculate the rate at which pipes fill or empty a tank, and how to combine these rates.
Net Rate Calculation – Calculating the net effect of multiple processes (filling and emptying) to determine the overall rate.
Time Calculation – Using the net rate to find the total time required to fill the tank.
