A tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hour
Practice Questions
Q1
A tank can be filled by a pipe in 8 hours and emptied by another pipe 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 can be filled by a pipe in 8 hours and emptied by another pipe in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
Step 1: Determine the rate at which the filling pipe works. It fills the tank in 8 hours, so its rate is 1 tank per 8 hours, or 1/8 of the tank per hour.
Step 2: Determine the rate at which the emptying pipe works. It empties the tank in 12 hours, so 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 from the filling rate: (1/8) - (1/12).
Step 4: To subtract these 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, the 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 a tank is filled or emptied by different pipes.
Combined Work Rate – Calculating the net effect of two pipes working together, one filling and one emptying.
