Expert: Abe Mantell - 12/25/2011

Question
Hello:

Here is my question:

15 workers can finish a job in 7 days.

If I want to find the number of days 21 workers can finish the job, the calculation becomes 1/(21 workers) X 15 workers X 7 days.

If the 21 and 15 are reduced to 7 and 5, by dividing 21 and 15 by 3, the calculation becomes 1/7 X 5 X 7 days, what do these two reduced terms (7 and 5) indicate or represent?

Do they represent 5 workers and 7 workers, as in (1/7 worker) X 5 workers X 7 days = 5 days?

I thank you for your reply.

Answer
We can think of the (15 workers)x(7 days) = 105 worker-days as the amount of work
needed to complete the 1 job.

So, having 21 workers gives (105 worker-days)/(21 workers) = 5 days

Thus, reducing the 15*7/21 to 5*7/7, the 5/7 can be interpreted the same way,
as you suggested.

Abe