If a tank can be filled by a pipe in 6 hours and another pipe can empty it in 4

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What’s inside this PDF?

Question: If a tank can be filled by a pipe in 6 hours and another pipe can empty it in 4 hours, how long will it take to fill the tank if both pipes are opened together?

Options:

2 hours
3 hours
4 hours
5 hours

Correct Answer: 3 hours

Solution:

The net rate is 1/6 - 1/4 = 2/12 - 3/12 = -1/12. Therefore, the tank will never fill.

If a tank can be filled by a pipe in 6 hours and another pipe can empty it in 4

Practice Questions

If a tank can be filled by a pipe in 6 hours and another pipe can empty it in 4 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 6 hours and another pipe can empty it in 4 hours, how long will it take to fill the tank if both pipes are opened together?

Step 1: Understand that one pipe fills the tank in 6 hours. This means it fills 1/6 of the tank in 1 hour.
Step 2: Understand that the other pipe empties the tank in 4 hours. This means it empties 1/4 of the tank in 1 hour.
Step 3: Calculate the filling rate of the first pipe: 1/6 of the tank per hour.
Step 4: Calculate the emptying rate of the second pipe: 1/4 of the tank per hour.
Step 5: To find the net effect when both pipes are open, subtract the emptying rate from the filling rate: (1/6) - (1/4).
Step 6: Convert the fractions to have a common denominator. The common denominator for 6 and 4 is 12.
Step 7: Rewrite 1/6 as 2/12 and 1/4 as 3/12.
Step 8: Now subtract: 2/12 - 3/12 = -1/12.
Step 9: The result -1/12 means that instead of filling, the tank is being emptied at a rate of 1/12 of the tank per hour.
Step 10: Since the net rate is negative, the tank will never fill when both pipes are opened together.

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 both filling and emptying.
Negative Rates – Recognizing that a negative net rate indicates that the tank will not fill.

If a tank can be filled by a pipe in 6 hours and another pipe can empty it in 4

What’s inside this PDF?

If a tank can be filled by a pipe in 6 hours and another pipe can empty it in 4

Practice Questions

Questions & Step-by-Step Solutions

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