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If a tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 ho

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Question: If a tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours, how long will it take to fill the tank if both pipes are opened together?

Options:

  1. 3 hours
  2. 4 hours
  3. 5 hours
  4. 6 hours

Correct Answer: 4 hours

Solution: 

The combined rate is (1/6 - 1/9) = (3-2)/18 = 1/18. Therefore, it will take 18 hours to fill the tank.

If a tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 ho

Practice Questions

Q1
If a tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours, how long will it take to fill the tank if both pipes are opened together?
  1. 3 hours
  2. 4 hours
  3. 5 hours
  4. 6 hours

Questions & Step-by-Step Solutions

If a tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours, how long will it take to fill the tank if both pipes are opened together?
  • Step 1: Determine the rate at which the filling pipe works. If it fills the tank in 6 hours, its rate is 1 tank per 6 hours, or 1/6 of the tank per hour.
  • Step 2: Determine the rate at which the emptying pipe works. If it empties the tank in 9 hours, its rate is 1 tank per 9 hours, or 1/9 of the tank per hour.
  • Step 3: Calculate the combined rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/6 - 1/9).
  • Step 4: To subtract the fractions, find a common denominator. The least common multiple of 6 and 9 is 18.
  • Step 5: Convert the rates to have the same denominator: (1/6 = 3/18) and (1/9 = 2/18).
  • Step 6: Now subtract the two rates: (3/18 - 2/18 = 1/18). This means that together, the pipes fill 1/18 of the tank in one hour.
  • Step 7: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 divided by (1/18) equals 18 hours.
  • Rate of Work – Understanding how to calculate the rate at which work is done when multiple processes are involved, such as filling and emptying a tank.
  • Combined Rates – Learning to combine rates of filling and emptying to find the net effect on the tank's fill level.
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