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.