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# Running at their respective constant rates, machine X takes

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Joined: 17 Sep 2006
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Running at their respective constant rates, machine X takes [#permalink]  29 Dec 2006, 18:51
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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?

Ａ　4
Ｂ　6
Ｃ　8
Ｄ　10
Ｅ　12
Intern
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Re: PS 1 [#permalink]  29 Dec 2006, 19:18
Iawfy wrote:
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?

Ａ　4
Ｂ　6
Ｃ　8
Ｄ　10
Ｅ　12

Explanation:
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.
x= 4.
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...
Senior Manager
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From the nature of the problem, I think your way of solving it is the most direct; the key is to be fast (=> practice...)
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