a very hard OG problem

[hongwang9703]

This question HAS to be a 700-800 level question because even with the explanation the OG gave me, I still do not understand it whatsoever... and I have tried to search this to see if it has been posted before but got no result.

here it is

Running at their respective constant rates, Machine X takes 2 days longer to produce W widgets than Machine Y. At theses rates, if the two machines together produce 5/4w widgets in 3 days, how many days would it take Machine X alone to produce 2w widgets?

answer is 12

[adam15]

let
ta=time required by machine A
tb=time required by machine B
we know that
w/ta+w/tb=5/4*(w/3)
after arrangement and some algebra we get;
ta=5/12tb
we know also that ta=2+tb or tb=ta-2
then
ta=2/7 for producing w
then for 2w it requires
4/7
thanks for comments and right answer if wrong

[thephoenix]

let d days for m/c Y to make w widgets
therefore d+2 days for m/c X to make w widgets

r1 rate for m/c X will w/(d+2)
r2 rate for m/c Y will w/d

combine rate w/(d+2)+w/d=(2wd+2w)/d(d+2)

now combinly x and y complete 5w/4 work in 3 days

i.e 3*[(2wd+2w)/d(d+2)]=5w/4

solving we get
(5d+6)(d-4)=0

taking d=4

x takes 6 days for w widgets
and therefore 12 days for 2w widgets

all this can be done in 2 min using MGmat word problems way of solving rate problem(the chart method)

[RoadtoIVY]

But I will still stick to the traditional way of doing this problem. i feel more comfortable.

[hongwang9703]

this is from the OG, so does that mean that it is very possible that we WILL get questions like these!!?

and please correct me if im wrong that this question is one of the hardest...