Machine X takes 2 days longer to produce w widgets than machine Y.?

Question

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?

Please provide answer and detailed explanation. Thanx

Answer 1

Let machine Y take d days to produce w widgets. Then Y runs at a rate of w/d, and machine X runs at a rate of w/(d+2).

Together they run at a rate of

(w/d) + w/(d+2) = (5w/4)/3 = 5w/12

=>d=4

Therefore machine X runs at a rate of w/6 widgets/day so would take 12 days to produce 2w widgets.