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A tank can be filled by a pipe in 6 hours and emptied by another pipe in 4 hours

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Question: 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?

Options:

  1. 2 hours
  2. 3 hours
  3. 4 hours
  4. 5 hours

Correct Answer: 4 hours

Solution: 

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

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?
  1. 2 hours
  2. 3 hours
  3. 4 hours
  4. 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.
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