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A tank is filled by two pipes in 12 hours and 16 hours respectively. If both pip

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Question: A tank is filled by two pipes in 12 hours and 16 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 5 hours
  2. 6 hours
  3. 7 hours
  4. 8 hours

Correct Answer: 7 hours

Solution: 

The combined rate is 1/12 + 1/16 = 7/48. Therefore, it will take 48/7 hours to fill the tank.

A tank is filled by two pipes in 12 hours and 16 hours respectively. If both pip

Practice Questions

Q1
A tank is filled by two pipes in 12 hours and 16 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
  1. 5 hours
  2. 6 hours
  3. 7 hours
  4. 8 hours

Questions & Step-by-Step Solutions

A tank is filled by two pipes in 12 hours and 16 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 6.857 hours (approximately 6 hours and 51 minutes)
  • Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour.
  • Step 2: The second pipe fills the tank in 16 hours, so its rate is 1/16 of the tank per hour.
  • Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/12 + 1/16.
  • Step 4: To add 1/12 and 1/16, find a common denominator. The least common multiple of 12 and 16 is 48.
  • Step 5: Convert 1/12 to a fraction with a denominator of 48: (1/12) * (4/4) = 4/48.
  • Step 6: Convert 1/16 to a fraction with a denominator of 48: (1/16) * (3/3) = 3/48.
  • Step 7: Now add the two fractions: 4/48 + 3/48 = 7/48.
  • Step 8: The combined rate of both pipes is 7/48 of the tank per hour.
  • Step 9: To find out how long it takes to fill the tank, take the reciprocal of the combined rate: 1 / (7/48) = 48/7 hours.
  • Step 10: Therefore, it will take 48/7 hours to fill the tank when both pipes are opened together.
  • Work Rate – Understanding how to calculate the combined work rate of multiple 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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