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A tank has two pipes. Pipe A can fill it in 6 hours and pipe B can empty it in 4

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Question: A tank has two pipes. Pipe A can fill it in 6 hours and pipe B can empty it in 4 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: 2 hours

Solution: 

The net rate is 1/6 - 1/4 = 2/12 - 3/12 = -1/12. The tank will never fill as the emptying rate is greater.

A tank has two pipes. Pipe A can fill it in 6 hours and pipe B can empty it in 4

Practice Questions

Q1
A tank has two pipes. Pipe A can fill it in 6 hours and pipe B can empty it in 4 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 has two pipes. Pipe A can fill it in 6 hours and pipe B can empty it in 4 hours. If both pipes are opened together, how long will it take to fill the tank?
  • Step 1: Understand that Pipe A fills the tank in 6 hours. This means it fills 1/6 of the tank in 1 hour.
  • Step 2: Understand that Pipe B empties the tank in 4 hours. This means it empties 1/4 of the tank in 1 hour.
  • Step 3: Calculate the filling rate of Pipe A: 1/6 of the tank per hour.
  • Step 4: Calculate the emptying rate of Pipe B: 1/4 of the tank per hour.
  • Step 5: Find the net rate when both pipes are opened together: Net rate = Filling rate - Emptying rate = 1/6 - 1/4.
  • Step 6: Convert the fractions to have a common denominator: 1/6 = 2/12 and 1/4 = 3/12.
  • Step 7: Subtract the emptying rate from the filling rate: 2/12 - 3/12 = -1/12.
  • Step 8: Interpret the result: A negative net rate (-1/12) means the tank is emptying faster than it is filling.
  • Step 9: Conclude that the tank will never fill because the emptying rate is greater than the filling rate.
  • Rate of Work – Understanding how to calculate the rates at which pipes fill or empty a tank.
  • Net Rate Calculation – Determining the overall effect of multiple rates working against each other.
  • Time Calculation – Calculating the time required to fill or empty a tank based on the net rate.
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