GeminiHeat wrote:
Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if the 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
One approach is to
assign a nice value to the job (w)Let's say that w =
12.
GIVEN:
Running at their respective constant rates, machine X takes 2 days longer to produce 12 widgets than machine YLet t = time for machine Y to produce
12 widgets
So, t+2 = time for machine X to produce
12 widgets
RATE = output/time
So, machine X's RATE =
12 widgets/(t + 2 days) = 12/(t+2) widgets per day
And machine Y's RATE =
12 widgets/(t days) = 12/t widgets per day
The two machines together produce 5w/4 widgets in 3 daysIn other words,
The two machines together produce 5(12)/4 widgets in 3 daysOr the two machines together produce 15 widgets in 3 days
This means the COMBINED RATE = 5 widgets per day
So, we can write: 12/(t+2) + 12/t = 5
Multiply both sides by (t+2)(t) to get: 12t + 12t + 24 = 5(t+2)(t)
Simplify: 24t + 24 = 5t² + 10t
Rearrange: 5t² - 14t - 24 = 0
Factor to get: (5t + 6)(t - 4) = 0
So, EITHER t = -6/5 OR t = 4
Since the time cannot be negative, it must be the case that t = 4
If t = 4, then it takes Machine Y 4 days to produce
12 widgets
And it takes Machine X 6 days to produce
12 widgets
How many days would it take machine X alone to produce 2w widgets?In other words,
how many days would it take machine X alone to produce 24 widgets? (since w =
12)
If it takes Machine X 6 days to produce
12 widgets, then it will take Machine X 12 days to produce
24 widgets
Answer: E
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep