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

Answer 1

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.