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A tank can be filled by a pipe in 4 hours and emptied by another pipe in 8 hours

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Question: A tank can be filled by a pipe in 4 hours and emptied by another pipe in 8 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: 5 hours

Solution: 

The net rate is 1/4 - 1/8 = 2/8 - 1/8 = 1/8. Therefore, it will take 8 hours to fill the tank.

A tank can be filled by a pipe in 4 hours and emptied by another pipe in 8 hours

Practice Questions

Q1
A tank can be filled by a pipe in 4 hours and emptied by another pipe in 8 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 4 hours and emptied by another pipe in 8 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 4 hours, so its rate is 1 tank per 4 hours, or 1/4 of the tank per hour.
  • Step 2: Determine the emptying rate of the second pipe. It empties the tank in 8 hours, so its rate is 1 tank per 8 hours, or 1/8 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: (1/4) - (1/8).
  • Step 4: To subtract these fractions, find a common denominator. The common denominator for 4 and 8 is 8. Convert 1/4 to 2/8.
  • Step 5: Now subtract: (2/8) - (1/8) = 1/8. This means that together, the pipes fill 1/8 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 (1/8) equals 8 hours.
  • 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, such as filling and emptying simultaneously.
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