A tank can be filled by a pipe in 10 hours and emptied by another pipe in 15 hou
Practice Questions
Q1
A tank can be filled by a pipe in 10 hours and emptied by another pipe in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
5 hours
6 hours
10 hours
12 hours
Questions & Step-by-Step Solutions
A tank can be filled by a pipe in 10 hours and emptied by another pipe in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 30 hours
Step 1: Determine the rate at which the filling pipe works. It fills the tank in 10 hours, so its rate is 1 tank per 10 hours, or 1/10 of the tank per hour.
Step 2: Determine the rate at which the emptying pipe works. It empties the tank in 15 hours, so its rate is 1 tank per 15 hours, or 1/15 of the tank per hour.
Step 3: Calculate the net rate when both pipes are open. The filling pipe adds 1/10 of the tank per hour, and the emptying pipe removes 1/15 of the tank per hour.
Step 4: To find the net rate, subtract the emptying rate from the filling rate: (1/10) - (1/15).
Step 5: Find a common denominator for the fractions. The common denominator for 10 and 15 is 30.
Step 6: Convert the rates: (1/10) = (3/30) and (1/15) = (2/30).
Step 7: Now subtract the two rates: (3/30) - (2/30) = (1/30).
Step 8: The net rate is 1/30 of the tank per hour, which means it takes 30 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.
