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Running at their respective constant rates, machine X takes

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Director
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Running at their respective constant rates, machine X takes [#permalink] New post 06 Feb 2006, 21:56
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?
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 [#permalink] New post 06 Feb 2006, 22:03
x's output per day = 1/(y+2)
y's output per day = 1/y

Working together, they produce (5/4)W in 3 days ==> 5/12W in 1 day

1/(y+2) + 1/y = 5/12 ==> Solve for y, y = 4 or -(6/5). Since y cannot be negative...y = 4

X's output per day is therefore 1/6 ==> it takes x 6 days to produce W ==> 12 days to produce 2W
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 [#permalink] New post 06 Feb 2006, 22:09
12 days! Good one but takes time to resolve

RATExy = Rx + Ry (Rate of x and Rate of y)
RATExy = W/Tx + W/Ty

Now if we assume Tx=n days than Ty will be n-2 days


RATExy = W/n + W/(n-2)

Now we know
Ratexy * 3 days= (5/4)W
3*(W/n + W/(n-2) = 5/4 W
3(1/n + 1(n-2)) = 5/4

solving for this one positive value of n will be 6 so to do 2W work it will take 12 days!
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 [#permalink] New post 06 Feb 2006, 22:17
Agree with TeHCM. 12 days.
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  [#permalink] 06 Feb 2006, 22:17
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Running at their respective constant rates, machine X takes

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