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GMAT数学题Running at their respective constant rates,machine X

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GMAT数学题
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.\x054
B.\x056
C.\x058
D.\x0510
E.\x0512
GMAT数学题Running at their respective constant rates,machine X
ANS 12..
Suppose machine Y produces w widgets in d days
so,X produces same in d+2 days
In 1 day Y produces w/d and X produces w/(d+2) widgets
Working together they will produce w/d + w/(d+2) = [2w(d+1)]/[d(d+2)] widgets in 1 day
in 3 days they produce 3*[2w(d+1)]/[d(d+2)] = 5w/4
Solve to get d =4
x produces w widgets in 4+2 = 6 days
so,2w widgets will be produces in 12 days
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