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?
let X take (x+2) days to complete 1 job .....eqn(1)
And Y take x days to complete 1 job
therefore, in 1 day X + Y can do (1/(x+2)) + (1/x) job
in 3 days X + Y completes 3*((1/(x+2)) + (1/x)) job
It is given that in 3 days X and Y togather complete 5/4 job
so, 3*((1/(x+2)) + (1/x)) = 5/4
Solve for x.
Now from eqn 1 x takes 4+2=6 days to complete 1 job
therefore 12 days to complete 2 jobs.
Took me quite awhile to solve for x. Wonder if there is an easier way...