If it takes 9 employees to complete 6 files in 14 hours - How many employees would it take to complete 4 files in 7 hours

Question

It's been a long time since I was in math, though I did enjoy it, so this is embarrassing.  This was a question posted for our work office as a little fun competition - After an extended period of time (to which I will not share), I cam to the conclusion that I felt was right.  Let me know so I know if I haven't completely lost my brain.

Answer 1

6 files in 14 hours is 3/7 files per hour for all 9 employees working together.

Assuming all the employees work at the same pace, the speed of each employee

is 3/7 divided by 9 = 3/7 * 1/9 = 1/7 * 1/3 = 1/21.

 

That is each employee working alone can complete 1 file in 21 hours.

 

So it will take 3 employees to complete 1 file in 7 hours.

 

Therefore, it will take 12 employees (4 times as many) to complete 4 files in 7 hours.