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A tank is filled by two pipes in 8 hours and 12 hours respectively. If both pipe

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Question: A tank is filled by two pipes in 8 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 4.8 hours
  2. 5 hours
  3. 6 hours
  4. 7 hours

Correct Answer: 4.8 hours

Solution: 

The combined rate is 1/8 + 1/12 = 5/24. Therefore, it will take 24/5 = 4.8 hours to fill the tank.

A tank is filled by two pipes in 8 hours and 12 hours respectively. If both pipe

Practice Questions

Q1
A tank is filled by two pipes in 8 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
  1. 4.8 hours
  2. 5 hours
  3. 6 hours
  4. 7 hours

Questions & Step-by-Step Solutions

A tank is filled by two pipes in 8 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 4.8 hours
  • Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 8 hours, so its rate is 1/8 of the tank per hour.
  • Step 2: The second pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour.
  • Step 3: Add the rates of both pipes together to find the combined rate. This is 1/8 + 1/12.
  • Step 4: To add 1/8 and 1/12, find a common denominator. The least common multiple of 8 and 12 is 24.
  • Step 5: Convert 1/8 to 3/24 and 1/12 to 2/24.
  • Step 6: Now add the two fractions: 3/24 + 2/24 = 5/24.
  • Step 7: The combined rate of both pipes is 5/24 of the tank per hour.
  • Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 / (5/24) = 24/5 hours.
  • Step 9: Calculate 24/5, which equals 4.8 hours.
  • Work Rate – Understanding how to calculate the combined work rate of multiple entities working together.
  • Fraction Addition – Adding fractions to determine the total rate of work done.
  • Time Calculation – Calculating the time taken to complete a task based on the combined work rate.
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