Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We have a combined worker problem. In such problems we use the equation:
Work (1 machine) + Work (2 machine) = Total Work.
We are given that the rate of machine A is 800/y and that when the two machines work together they take x hours to produce 800 nails. We can let the rate of machine B = 800/b, where b = the number of hours that it takes machine B to produce 800 nails.
Since work = rate x time, we can calculate the work done by machine A and machine B when working together.
Work of machine A = (800/y)(x) = 800x/y
Work of machine B = (800/b)(x) = 800x/b
Now we can substitute the two work values of A and B into the combined work equation.
Work (1 machine) + Work (2 machine) = Total Work.
800x/y + 800x/b = 800
Multiplying the entire equation by yb we have:
800xb + 800xy = 800yb
xb + xy = yb
xy = yb – xb
xy = b(y – x)
xy/(y – x)= b
Answer: E
