Multiple choice

A can do a piece of work in $14$ days and B in $21$ days. They begin together, but $3$ days before the completion of the work, A leaves off. In how many days is the work complete?

  1. $10\ days$
  2. $10\dfrac {1}{5} days$
  3. $15\ days$
  4. $7\ days$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate is 1/14, B's rate is 1/21. Let total days be x. B works for x days, A works for x-3 days. (x-3)/14 + x/21 = 1. Multiply by 42: 3(x-3) + 2x = 42. 3x - 9 + 2x = 42, 5x = 51, x = 10.2 days.

AI explanation

Assume the total work is the least common multiple of 14 and 21, which is 42 units. A's rate is 42 divided by 14, equaling 3 units per day, and B's rate is 42 divided by 21, equaling 2 units per day. Since A leaves 3 days before completion, B works alone for the last 3 days to complete 3 multiplied by 2, which is 6 units. The remaining 36 units were completed by A and B working together at a combined rate of 5 units per day, taking 36 divided by 5, or 7.2 days. Adding the 7.2 days to the final 3 days, the total time is 10.2 days, which equals 10 and 1/5 days.

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