A tank can be filled by a pipe in 6 hours and emptied by another pipe in 4 hours
Practice Questions
Q1
A tank can be filled by a pipe in 6 hours and emptied by another pipe in 4 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 6 hours and emptied by another pipe in 4 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 12 hours
Step 1: Understand that one pipe fills the tank and the other pipe empties it.
Step 2: Determine the rate at which the filling pipe works. It fills the tank in 6 hours, so its rate is 1/6 of the tank per hour.
Step 3: Determine the rate at which the emptying pipe works. It empties the tank in 4 hours, so its rate is 1/4 of the tank per hour.
Step 4: Calculate the net rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/6) - (1/4).
Step 5: To subtract these fractions, find a common denominator. The common denominator for 6 and 4 is 12.
Step 6: Convert the rates to have the same denominator: (1/6) = 2/12 and (1/4) = 3/12.
Step 7: Now subtract the two rates: (2/12) - (3/12) = -1/12.
Step 8: The negative result (-1/12) means that the emptying pipe is stronger than the filling pipe, so the tank will never fill.
Rate of Work – Understanding how to calculate the rate at which a tank is filled or emptied by different pipes.
Combined Rates – Calculating the net effect of multiple rates working together, including filling and emptying.
