# Working simultaneously at their respective constant rates, Machines A and B…

# 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**