alohagirl wrote:

Running at their respective constant rates, machine X takes 2 days longer to produc ew widgets than machine Y. At these rates, if two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets

A. 4

B. 6

C. 8

D. 10

E. 12

I seem to have difficult time with work problem

!

Backsolving strategy worked out best for me; didn't have to deal w/ quadratics or anything.

let w = 36 (number divisible by 4); 2w = 72

Speed of A & B = 5/4 w in 3 days or 15 w/day.

Now backsolve starting w/ choice C.

Let time taken by A to produce 2w=72 widgets be 8 days

Therefore, speed of A = 9 widgets/day

Therefore, speed of B = 15-9 = 6 widgets/day

Therefore, time taken by B to produce 2w = 72 widgets = 12 days.

Time taken by A to produce 1 w = 4 days

Time taken by B to produce 1 w = 6 days

Since B is taking longer than A, C is wrong.

Backsolve using E.

Let time taken by A to produce 2w=72 widgets be 12 days

Therefore, speed of A = 6 widgets/day

Therefore, speed of B = 15-6 = 9 widgets/day

Therefore, time taken by B to produce 2w = 72 widgets = 8 days.

Time taken by A to produce 1 w = 6 days

Time taken by B to produce 1 w = 4 days

This is our answer.