If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 9 ho
Practice Questions
Q1
If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 9 hours, how long will it take to fill the tank if both pipes are opened together?
2 hours
3 hours
4 hours
5 hours
Questions & Step-by-Step Solutions
If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 9 hours, how long will it take to fill the tank if both pipes are opened together?
Step 1: Determine the filling rate of the first pipe. If the tank can be filled in 3 hours, the filling rate is 1 tank per 3 hours, or 1/3 of the tank per hour.
Step 2: Determine the emptying rate of the second pipe. If the tank can be emptied in 9 hours, the emptying rate is 1 tank per 9 hours, or 1/9 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: (1/3) - (1/9).
Step 4: To subtract these fractions, find a common denominator. The common denominator for 3 and 9 is 9. Convert 1/3 to 3/9.
Step 6: The net rate of filling the tank is 2/9 of the tank per 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 (2/9) equals 9/2 hours.
Step 8: Simplify 9/2 hours to get 4.5 hours.
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 – Calculating the net effect of two pipes working together, one filling and one emptying, by subtracting their rates.
