Multiple choice

'A' can do a piece of work in 6 days and 'B' can do it in 8 days. How long (in days) will both 'A' and 'B' take to do the work, if they work together?

  1. 7/24

  2. 24/7

  3. 7/12

  4. 12/7

  5. 7/48
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B Correct answer
Explanation

A's rate = 1/6 work/day. B's rate = 1/8 work/day. Combined rate = 1/6 + 1/8 = 4/24 + 3/24 = 7/24 work/day. Time taken = 24/7 days.

AI explanation

Using the fraction addition method, the combined work done by A and B in one day is 1 divided by 6 plus 1 divided by 8. Finding a common denominator of 24 gives 4 divided by 24 plus 3 divided by 24, which equals 7 divided by 24. The total time taken to complete the work together is the reciprocal of this sum, which is 24 divided by 7 days.

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