CrackSAT - SAT Prep Classes, Study Material

Please help.

If John can complete a project in 30 days and Joe in 60 days, how long will they take to complete the project if they worked on the project on alternate days? John starts working on the first day.

I got an answer of 20 days. However OA is 40.

Hi Alex

A delayed response to your query. Apologies.

Your answer of 20 days is correct if they worked together. However, this question states that they worked on it on alternate days. i.e. , John works alone on day 1. Joe works alone on day 2 and then John works alone on day 3 and so on.

As John could complete 1/30th of the work in a day and Joe could complete 1/60th of the work in a day,
at the end of day 2, they would have completed (1/30 + 1/60)th of the work.

i.e., ((2 + 1)/60)th of the work gets done in 2 days
3/60th or 1/20th of the work gets done in 2 DAYS and not in 1 DAY.
Hence, they will take 20 * 2 = 40 days to complete the task.

Will the answer not be different depending on who started working first?

John and Joe complete do not work at the same rate.

Good point.

No. It will not make a difference in this case. 1/30 + 1/60 = 1/20. If the answer had been 3/20 or some such number where the reciprocal of the value would not have been an integer, it would have mattered as to who started first.

In this case, no.