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If A can complete a task in 4 hours and B can complete the same task in 6 hours,

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Question: If A can complete a task in 4 hours and B can complete the same task in 6 hours, how long will it take them to complete the task together?

Options:

  1. 2.4 hours
  2. 2.5 hours
  3. 3 hours
  4. 3.6 hours

Correct Answer: 2.5 hours

Solution: 

The combined rate is 1/4 + 1/6 = 5/12, so together they complete the task in 12/5 hours, which is 2.4 hours.

If A can complete a task in 4 hours and B can complete the same task in 6 hours,

Practice Questions

Q1
If A can complete a task in 4 hours and B can complete the same task in 6 hours, how long will it take them to complete the task together?
  1. 2.4 hours
  2. 2.5 hours
  3. 3 hours
  4. 3.6 hours

Questions & Step-by-Step Solutions

If A can complete a task in 4 hours and B can complete the same task in 6 hours, how long will it take them to complete the task together?
  • Step 1: Determine how much of the task A can complete in one hour. Since A can complete the task in 4 hours, A's rate is 1/4 of the task per hour.
  • Step 2: Determine how much of the task B can complete in one hour. Since B can complete the task in 6 hours, B's rate is 1/6 of the task per hour.
  • Step 3: Add A's rate and B's rate together to find their combined rate. This is 1/4 + 1/6.
  • Step 4: To add 1/4 and 1/6, find a common denominator. The least common multiple of 4 and 6 is 12.
  • Step 5: Convert 1/4 to a fraction with a denominator of 12. This is 3/12.
  • Step 6: Convert 1/6 to a fraction with a denominator of 12. This is 2/12.
  • Step 7: Now add the two fractions: 3/12 + 2/12 = 5/12.
  • Step 8: The combined rate of A and B is 5/12 of the task per hour.
  • Step 9: To find out how long it takes them to complete the entire task together, take the reciprocal of their combined rate. This means you calculate 1 divided by (5/12).
  • Step 10: 1 divided by (5/12) is the same as multiplying by the reciprocal, which is 12/5.
  • Step 11: 12/5 hours is equal to 2.4 hours.
  • Work Rate – Understanding how to calculate the combined work rate of two individuals completing a task.
  • Fraction Addition – Adding fractions with different denominators to find a common work rate.
  • Time Calculation – Converting the combined work rate into time taken to complete the task.
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