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If a tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 ho

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Question: If a tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 hours, how long will it take to fill the tank if both pipes are opened together?

Options:

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

Correct Answer: 2 hours

Solution: 

The net rate is 1/4 - 1/6 = 3/12 - 2/12 = 1/12. Therefore, it will take 12 hours to fill the tank.

If a tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 ho

Practice Questions

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

Questions & Step-by-Step Solutions

If a tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 hours, how long will it take to fill the tank if both pipes are opened together?
  • Step 1: Determine the filling rate of the first pipe. It can fill 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 can empty 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. This is done by subtracting the emptying rate from the filling rate: (1/4) - (1/6).
  • Step 4: To subtract the fractions, find a common denominator. The common denominator for 4 and 6 is 12.
  • Step 5: Convert the rates to have the common denominator: (1/4) becomes (3/12) and (1/6) becomes (2/12).
  • Step 6: Now subtract the two fractions: (3/12) - (2/12) = (1/12).
  • Step 7: The net rate of filling the tank is 1/12 of the tank per hour.
  • Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 divided by (1/12) equals 12 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 – Calculating the net effect of two pipes working together, one filling and one emptying, by finding their individual rates and combining them.
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