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If a tank is filled by a pipe in 6 hours and another pipe can empty it in 9 hour

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

Options:

  1. 4 hours
  2. 5 hours
  3. 6 hours
  4. 7 hours

Correct Answer: 6 hours

Solution: 

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

If a tank is filled by a pipe in 6 hours and another pipe can empty it in 9 hour

Practice Questions

Q1
If a tank is filled by a pipe in 6 hours and another pipe can empty it in 9 hours, how long will it take to fill the tank if both pipes are opened together?
  1. 4 hours
  2. 5 hours
  3. 6 hours
  4. 7 hours

Questions & Step-by-Step Solutions

If a tank is filled by a pipe in 6 hours and another pipe can empty it 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 net 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 these 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) becomes (3/18) and (1/9) becomes (2/18).
  • Step 6: Now subtract the two fractions: (3/18) - (2/18) = (1/18). This means the net rate is 1/18 of the tank per hour.
  • Step 7: To find out how long it takes to fill the tank at this net rate, take the reciprocal of the net rate: 1 divided by (1/18) equals 18 hours.
  • Rate of Work – Understanding how to calculate the rate at which pipes fill or empty a tank.
  • Combined Work Rate – Calculating the net effect of multiple rates working together.
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