heyholetsgo wrote:
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.
A. 4
B. 6
C. 8
D. 10
E. 12
Not sure if it is weird, but I tried a different approach:
Rate of doing work by X = x widgets per day
Rate of doing work by Y = y widgets per day
According to the question,
Time taken by machine X to produce w widgets is 2 days more than time taken by machine Y to produce w widgets
time = (items produced)/(rate) { "time = distance/speed" analogy}
Therefore,
(w/x) = (w/y) + 2 ...... (1)
Also, working simultaneously, X and Y produce 5w/4 widgets in 3 days
i.e. 3(w/x) + 3(w/x) = 5w/4 ...... (2) {distance = speed * time}
Substituting (1) in (2):
(w/x) +(w/x) -2 = 5w/12
2(w/x) = (5w/12) + 2
Note that (2(w/x)) is the time taken by X to produce 2w widgets, which is what we need to find out.
Since all answers are in integers, we know that (5w/12) + 2 must be an integer
Therefore, w = {12, 24, 36, ...}
w = 12; 2(w/x) = 7 - Does not match with any option
w = 24; w(w/x) = 12 - Matches with (E)
All other options are less than 12, so not possible. Therefore, the correct answer is (E)