A tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 hours
Practice Questions
Q1
A tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 hours. If both pipes are opened together, how long will it take to fill the tank?
2 hours
3 hours
4 hours
5 hours
Questions & Step-by-Step Solutions
A tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 12 hours
Step 1: Determine the filling rate of the first pipe. It fills the tank in 4 hours, so its rate is 1 tank per 4 hours, or 1/4 tank per hour.
Step 2: Determine the emptying rate of the second pipe. It empties the tank in 6 hours, so its rate is 1 tank per 6 hours, or 1/6 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: (1/4) - (1/6).
Step 4: To subtract the fractions, find a common denominator. The common denominator for 4 and 6 is 12.
Step 5: Convert the rates to have the common denominator: (1/4) = 3/12 and (1/6) = 2/12.
Step 6: Now subtract the two rates: (3/12) - (2/12) = 1/12.
Step 7: The net rate of filling the tank is 1/12 tank per hour, which means it takes 12 hours to fill the tank when both pipes are open.
Rate of Work – Understanding how to calculate the rate at which work is done when multiple processes are involved, such as filling and emptying a tank.
Combined Rates – Learning to combine rates of filling and emptying to find the net effect on the tank's water level.
Time Calculation – Applying the formula for time based on the net rate of work to determine how long it will take to fill the tank.
