Check this thread out:

https://www.beatthegmat.com/widgets-t40224.html#166925

I typically solve this algebraically, but it may not be the fastest way

let d be the num days machine Y takes to build w widgets

Machine X
days= d+2
widgets= w
rate = w/(d+2)

Machine Y
days= d
widgets= w
rate = w/(d)

Machine X & Y together
days= 3
widgets= 5/4w
rate = (5/4w)/3 = 5/12w

so rate of X & Y = w/(d+2) + w/d = 5/12w
1/(d+2) + 1/d = 5/12
(2d+2)/(d^2+2d) = 5/12
24d+24=5d^2+10d
0=5d^2-14d-24
0=(5d+6)(d-4)
d=-ve or 4

so X take d+2=4+2=6 to make w widgets, so to make 2w widgets it takes 12 days

hope that helps


solving for d

x=y+2

w/x+w/y=5/4 * 1/3 days

rate then is:

w/(y+2)+w/y=5/12

solve for y. the w's will cancel out.

0=5y^2-14y-24
0=(5y+6)(y-4)

y has to equal 4.

x=4+2=6

w/6=2w/x
x=12

cheers.

Thank u