Multiple choice

John alone could complete a given task in 20 days. Jane would take only 12 days to complete the same task alone. John and Jane set out to complete the task by beginning to work together. However, Jane left 4 days before the work was completed. In how many days was the work completed from the time John and Jane started to work on it together?

  1. 6

  2. 10

  3. 8

  4. 7.5

  5. 3.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

John's rate is 1/20, Jane's is 1/12. Let T be total time. John works for T days, Jane for T-4 days. (T/20) + (T-4)/12 = 1. Multiply by 60: 3T + 5(T-4) = 60. 3T + 5T - 20 = 60, 8T = 80, T = 10.

AI explanation

John's daily work rate is 1/20 and Jane's is 1/12. Let the total time taken to complete the task be x days, meaning John worked for x days and Jane worked for x - 4 days. The work equation is x/20 + (x - 4)/12 = 1, which simplifies to 3x + 5x - 20 = 60. Solving for x gives 8x = 80, so the work was completed in 10 days.

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