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A tank can be filled by a pipe in 3 hours and emptied by another pipe in 6 hours

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Question: A tank can be filled by a pipe in 3 hours and emptied by another pipe in 6 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: 3 hours

Solution: 

The net rate is 1/3 - 1/6 = 2/6 - 1/6 = 1/6. Therefore, it will take 6 hours to fill the tank.

A tank can be filled by a pipe in 3 hours and emptied by another pipe in 6 hours

Practice Questions

Q1
A tank can be filled by a pipe in 3 hours and emptied by another pipe in 6 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 6 hours. If both pipes are opened together, how long will it take to fill the tank?
  • Step 1: Determine the filling rate of the first pipe. 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 emptying rate of the second pipe. It empties the tank in 6 hours, so its rate is 1 tank per 6 hours, or 1/6 of the tank per hour.
  • Step 3: Calculate the net rate when both pipes are opened together. The net rate is the filling rate minus the emptying rate: (1/3) - (1/6).
  • Step 4: To subtract these fractions, find a common denominator. The common denominator for 3 and 6 is 6. Convert 1/3 to 2/6.
  • Step 5: Now subtract: (2/6) - (1/6) = 1/6. This means that together, the pipes fill 1/6 of the tank in one hour.
  • Step 6: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 divided by (1/6) equals 6 hours.
  • Rate of Work – Understanding how to calculate the rate at which a tank is filled or emptied by different pipes.
  • Combined Work Rate – Calculating the net effect of multiple processes working together, such as filling and emptying a tank.
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