A tank can be filled by a pipe in 7 hours and emptied by another pipe in 14 hour
Practice Questions
Q1
A tank can be filled by a pipe in 7 hours and emptied by another pipe in 14 hours. If both pipes are opened together, how long will it take to fill the tank?
4 hours
5 hours
6 hours
7 hours
Questions & Step-by-Step Solutions
A tank can be filled by a pipe in 7 hours and emptied by another pipe in 14 hours. If both pipes are opened together, how long will it take to fill the tank?
Step 1: Determine the filling rate of the first pipe. It fills the tank in 7 hours, so its rate is 1 tank per 7 hours, or 1/7 of the tank per hour.
Step 2: Determine the emptying rate of the second pipe. It empties the tank in 14 hours, so its rate is 1 tank per 14 hours, or 1/14 of the tank per hour.
Step 3: Calculate the net rate when both pipes are opened together. The net rate is the filling rate minus the emptying rate: (1/7) - (1/14).
Step 4: To subtract the fractions, find a common denominator. The common denominator for 7 and 14 is 14. Convert 1/7 to 2/14.
Step 5: Now subtract: (2/14) - (1/14) = 1/14. This means that together, the pipes fill 1/14 of the tank in one hour.
Step 6: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 divided by (1/14) equals 14 hours.
Rate of Work – Understanding how to calculate the rate at which a tank can be filled or emptied by different pipes.
Combined Work Rate – Calculating the net effect of two pipes working together, one filling and one emptying.
