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A tank can be filled by a pipe in 9 hours and emptied by another pipe in 3 hours

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Question: A tank can be filled by a pipe in 9 hours and emptied by another pipe in 3 hours. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 2.25 hours
  2. 3 hours
  3. 4.5 hours
  4. 5 hours

Correct Answer: 2.25 hours

Solution: 

The net rate is 1/9 - 1/3 = 1/9 - 3/9 = -2/9. Therefore, the tank will never fill.

A tank can be filled by a pipe in 9 hours and emptied by another pipe in 3 hours

Practice Questions

Q1
A tank can be filled by a pipe in 9 hours and emptied by another pipe in 3 hours. If both pipes are opened together, how long will it take to fill the tank?
  1. 2.25 hours
  2. 3 hours
  3. 4.5 hours
  4. 5 hours

Questions & Step-by-Step Solutions

A tank can be filled by a pipe in 9 hours and emptied by another pipe in 3 hours. If both pipes are opened together, how long will it take to fill the tank?
  • 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 9 hours, so its rate is 1/9 of the tank per hour.
  • Step 3: Determine the rate at which the emptying pipe works. It empties the tank in 3 hours, so its rate is 1/3 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: (1/9) - (1/3).
  • Step 5: Convert 1/3 to have a common denominator with 1/9. 1/3 is the same as 3/9.
  • Step 6: Now, subtract the rates: (1/9) - (3/9) = -2/9.
  • Step 7: The negative result (-2/9) means that the tank is being emptied faster than it is being filled.
  • Step 8: Conclude that if both pipes are opened together, 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.
  • Time Calculation – Determining the time taken to fill the tank based on the net rate of filling.
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