Multiple choice

A can do 1/5 of a job in 10 days and B can do 1/3 of the job in 25 days. In how many days can they do half of the job working together?

  1. 30

  2. 45

  3. 15

  4. 20
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does 1/5 in 10 days, so full job in 50 days. B does 1/3 in 25 days, so full job in 75 days. Combined rate = 1/50 + 1/75 = (3+2)/150 = 5/150 = 1/30. To do half the job, they need (1/2) / (1/30) = 15 days.

AI explanation

A completes the entire job in 5 times 10, or 50 days, giving a one-day work rate of 1 over 50. B completes the entire job in 3 times 25, or 75 days, giving a one-day work rate of 1 over 75. Their combined one-day work rate is 1 over 50 plus 1 over 75, which equals 5 over 150 or 1 over 30. To complete half of the job, divide 1 over 2 by their combined daily rate of 1 over 30, which results in 15 days.

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