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Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 hours.

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Question: Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 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: 3 hours

Solution: 

The combined rate is 1/6 + 1/9 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.

Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 hours.

Practice Questions

Q1
Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 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

Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 3.6 hours
  • Step 1: Determine the rate at which Pipe A fills the tank. Since Pipe A can fill 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 Pipe B fills the tank. Since Pipe B can fill the tank in 9 hours, its rate is 1 tank per 9 hours, or 1/9 of the tank per hour.
  • Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/6 + 1/9.
  • Step 4: To add 1/6 and 1/9, find a common denominator. The least common multiple of 6 and 9 is 18.
  • Step 5: Convert 1/6 to have a denominator of 18: (1/6) * (3/3) = 3/18.
  • Step 6: Convert 1/9 to have a denominator of 18: (1/9) * (2/2) = 2/18.
  • Step 7: Now add the two fractions: 3/18 + 2/18 = 5/18.
  • Step 8: The combined rate of both pipes is 5/18 of the tank per hour.
  • Step 9: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 / (5/18) = 18/5 hours.
  • Step 10: Simplify 18/5 to get 3.6 hours.
  • Work Rate – Understanding how to calculate the combined work rate of two or more entities working together.
  • Fraction Addition – Adding fractions with different denominators to find a common rate.
  • Time Calculation – Calculating the total time taken based on the combined work rate.
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