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

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Question: A tank can be filled by a pipe in 3 hours and emptied by another pipe in 9 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: 2 hours

Solution: 

The net rate is 1/3 - 1/9 = 3/9 - 1/9 = 2/9. Therefore, it will take 9/2 hours or 4.5 hours.

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

Practice Questions

Q1
A tank can be filled by a pipe in 3 hours and emptied by another pipe in 9 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 3 hours and emptied by another pipe in 9 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 3 hours, so its rate is 1 tank per 3 hours, or 1/3 of the tank per hour.
  • Step 2: Determine the rate at which the emptying pipe works. It empties the tank in 9 hours, so its rate is 1 tank per 9 hours, or 1/9 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: (1/3) - (1/9).
  • Step 4: To subtract these fractions, find a common denominator. The common denominator for 3 and 9 is 9. Convert 1/3 to 3/9.
  • Step 5: Now subtract: (3/9) - (1/9) = (3 - 1)/9 = 2/9.
  • Step 6: The net rate of filling the tank is 2/9 of the tank per 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 (2/9) equals 9/2 hours.
  • Step 8: Simplify 9/2 hours to get 4.5 hours.
  • Rate of Work – Understanding how to calculate the rate at which work is done when multiple processes are involved.
  • Combined Work Rate – Calculating the net effect of filling and emptying processes when both are operating simultaneously.
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