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 54 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? A4 B6 C8 D10 E12

Step-by-step explanation:

Work done = rate * time

let time taken by X to produce w widgets be t days

rate = w/t

Since X take 2 days longer rate for Y would be

rate = w/t-2

combined rate is (w/t+w/t-2)

Since in 3 days both x and y can produce 5w/4

(w/t+w/t-2) = 5w/4

5t2 - 34t + 24=0

(t-6) (t-4/5) = 0

t=6 or t=4/5 (not possible because t-2 (time taken by Y) comes out to be - 6/5 which is not possible)

so t=6 days which is the time taken by X to produce w widgets

so time taken to produce 2w widgets will be 12 days.