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A tank is filled by two pipes in 9 hours and 18 hours respectively. If both pipe

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Question: A tank is filled by two pipes in 9 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 6 hours
  2. 7 hours
  3. 8 hours
  4. 9 hours

Correct Answer: 6 hours

Solution: 

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

A tank is filled by two pipes in 9 hours and 18 hours respectively. If both pipe

Practice Questions

Q1
A tank is filled by two pipes in 9 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
  1. 6 hours
  2. 7 hours
  3. 8 hours
  4. 9 hours

Questions & Step-by-Step Solutions

A tank is filled by two pipes in 9 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
  • Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 9 hours, so its rate is 1/9 of the tank per hour.
  • Step 2: The second pipe fills the tank in 18 hours, so its rate is 1/18 of the tank per hour.
  • Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/9 + 1/18.
  • Step 4: To add 1/9 and 1/18, find a common denominator. The least common multiple of 9 and 18 is 18.
  • Step 5: Convert 1/9 to have a denominator of 18. This gives us 2/18.
  • Step 6: Now add the two fractions: 2/18 + 1/18 = 3/18.
  • Step 7: Simplify 3/18 to 1/6. This means together, both pipes fill 1/6 of the tank in one hour.
  • Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of 1/6, which is 6 hours.
  • Work Rate – Understanding how to calculate the rate of work done by multiple entities working together.
  • Fraction Addition – Adding fractions to find a combined rate of work.
  • Time Calculation – Calculating the total time required to complete a task based on combined rates.
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