Problem Solving

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

I would choose E.

X alone takes 12 days to produce 2w widgets.

Let n be the number of days Y takes to produce w widgets. So rate of work for Y is w/n.

X takes 2 more days than Y to produce w widgets. So, rate of work for X is w/(n+2).

Both combined can produce 5/4w widgets in 3 days - so, in one day they both can produce 5/12w widgets.

w/n + w/(n+2) = 5/12w

Solving for n (we can eliminate w in the process) will give us n=4.

X takes 6 days to produce w widgets

So, 12 days to produce 2w widgets.

sonu_thekool wrote:I would choose E.

X alone takes 12 days to produce 2w widgets.

Let n be the number of days Y takes to produce w widgets. So rate of work for Y is w/n.

X takes 2 more days than Y to produce w widgets. So, rate of work for X is w/(n+2).

Both combined can produce 5/4w widgets in 3 days - so, in one day they both can produce 5/12w widgets.

w/n + w/(n+2) = 5/12w

Solving for n (we can eliminate w in the process) will give us n=4.

X takes 6 days to produce w widgets

So, 12 days to produce 2w widgets.

Thank you, sonu_thekool, for solving the problem. The answer is indeed E.

My Algebra is a little rusty, so can you clue me in how you get 4 when you use 1/n + 1/(n+2) = 5/12?

Thanks!

jkwan wrote:My Algebra is a little rusty, so can you clue me in how you get 4 when you use 1/n + 1/(n+2) = 5/12?

Thanks!

No problem. Here are the steps.

Taking common denominator. n * (n+2) = n^2 + 2n
Left hand side of the equation would be n+2+n / (n^2 +2n)

Cross multiplying
(2n+2)*12 = 5(n^2 + 2n)
24n + 24 = 5n^2 + 10n
5n^2 - 14n -24 = 0

this equation can be split into two
(5n-20) and (6n-24) each equal to 0

So, 5n = 20 and n = 4.

Hope this is clear.