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Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes a

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Question: Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 6 hours
  2. 7.5 hours
  3. 8 hours
  4. 9 hours

Correct Answer: 7.5 hours

Solution: 

The combined rate is 1/10 + 1/15 = 1/6. Therefore, it will take 6 hours to fill the tank.

Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes a

Practice Questions

Q1
Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
  1. 6 hours
  2. 7.5 hours
  3. 8 hours
  4. 9 hours

Questions & Step-by-Step Solutions

Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 6 hours
  • Step 1: Understand that each pipe has a filling rate. The first pipe fills the tank in 10 hours, so its rate is 1/10 of the tank per hour.
  • Step 2: The second pipe fills the tank in 15 hours, so its rate is 1/15 of the tank per hour.
  • Step 3: To find the combined rate of both pipes, add their rates together: 1/10 + 1/15.
  • Step 4: To add the fractions, find a common denominator. The least common multiple of 10 and 15 is 30.
  • Step 5: Convert the fractions: 1/10 becomes 3/30 and 1/15 becomes 2/30.
  • Step 6: Now add the fractions: 3/30 + 2/30 = 5/30.
  • Step 7: Simplify 5/30 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 combined work rate of multiple entities working together.
  • Fraction Addition – Applying the concept of 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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