Last Updated on May 3, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This problem is what we would call a combined worker problem, where
Work (of machine 1) + Work (of machine 2) = Total Work Completed
In this case,
Work (of A) + Work (of B) = 800
We know that machines A and B produce 800 nails in x hours. Thus, the TIME that machine A and B work together is x hours. We are also given that Machine A produces 800 in y hours. Thus, the rate for machine A is 800/y. Since we do not know the rate for machine B, we can label the rate as 800/B, where B is the number of hours it takes Machine B to produce 800 nails.
To better organize our information we can set up a rate x time = work chart:
We now can say:
Work (of A) + Work (of B) = 800
800x/y + 800x/B = 800
To cancel out our denominators, we can multiply the entire equation by yB. This gives us:
800xB + 800xy= 800yB
xB + xy = yB
xy = yB – xB
xy = B(y – x)
xy /(y-x) = B
Answer: E
