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If A can complete a task in 30 days and B can complete it in 45 days, what is th

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Question: If A can complete a task in 30 days and B can complete it in 45 days, what is the average time taken by A and B to complete the task together?

Options:

  1. 20 days
  2. 25 days
  3. 35 days
  4. 40 days

Correct Answer: 25 days

Solution: 

Combined work rate = 1/30 + 1/45 = 5/90. Time taken = 90/5 = 18 days.

If A can complete a task in 30 days and B can complete it in 45 days, what is th

Practice Questions

Q1
If A can complete a task in 30 days and B can complete it in 45 days, what is the average time taken by A and B to complete the task together?
  1. 20 days
  2. 25 days
  3. 35 days
  4. 40 days

Questions & Step-by-Step Solutions

If A can complete a task in 30 days and B can complete it in 45 days, what is the average time taken by A and B to complete the task together?
  • Step 1: Determine the work rate of A. A can complete the task in 30 days, so A's work rate is 1/30 of the task per day.
  • Step 2: Determine the work rate of B. B can complete the task in 45 days, so B's work rate is 1/45 of the task per day.
  • Step 3: Add the work rates of A and B together to find their combined work rate. This is 1/30 + 1/45.
  • Step 4: To add the fractions, find a common denominator. The least common multiple of 30 and 45 is 90.
  • Step 5: Convert the fractions to have the common denominator of 90. A's work rate becomes 3/90 and B's work rate becomes 2/90.
  • Step 6: Now add the two fractions: 3/90 + 2/90 = 5/90.
  • Step 7: The combined work rate of A and B is 5/90, which simplifies to 1/18 of the task per day.
  • Step 8: To find the time taken to complete the task together, take the reciprocal of the combined work rate: 1 divided by (5/90) equals 90/5.
  • Step 9: Calculate 90/5, which equals 18 days.
  • Work Rate – Understanding how to calculate the combined work rate of two individuals based on their individual completion times.
  • Fraction Addition – Adding fractions with different denominators to find a common work rate.
  • Reciprocal Calculation – Using the reciprocal of the combined work rate to determine the total time taken to complete the task.
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