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# machine X and Y run at different constant rates, and machine

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Manager
Joined: 30 Mar 2007
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machine X and Y run at different constant rates, and machine [#permalink]  01 Jun 2007, 11:25
machine X and Y run at different constant rates, and machine x can complete a certain job in 9 hours. machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine y working alone to complete the entire job?
Ａ）１８　Ｂ）１３ 1/2 C)7 1/5
Manager
Joined: 22 May 2007
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I believe it is C.

1/9 + 1/x =1/4 --->>> x=24/5 so in 24/5 hours, the other machine completes 6/9 of the work.

24/5 divided by 6/9 gives us the answer of 36/5 or 7 1/5.

What is OA?
Manager
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That's right! By backsolving I get 18 or A.

I got fooled, gotta work on these problems ))
Manager
Joined: 14 Mar 2007
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A. 18

Mch X can do the job in 9 hours
in 1 hour = 1/9
Working alone for 3 hours = 3/9
So 1-3/9 = 6/9 of the job is left
Mch X and Mch Y do 6/9 in 4 hours

Now lets assume Mch Y will do the job in y hours
In 1 hour = 1/y

So both of them together in 1 hour
1/9+1/y = 9+y/9y

In 4 hours they do
4(9+y)/9y
This is equal to 6/9
Solve to get y = 18
Director
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Re: work question [#permalink]  01 Jun 2007, 16:09
Jamesk486 wrote:
machine X and Y run at different constant rates, and machine x can complete a certain job in 9 hours. machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine y working alone to complete the entire job?
Ａ）１８　Ｂ）１３ 1/2 C)7 1/5
I noticed that not all of the answer choices were listed. I think the answer is 12. If not, will someone tell me why we couldn't solve the prob this way:

x rate = 1/9, x works for 3 hrs and completes 1/3 of the work.

now, x and y wrapped up the remaining 2/3 of work in 4 hrs:
r(4)=2/3 ==> r = 2/3(1/4) = 2/12 = 1/6.

so, x's rate is 1/9 and x's and y's combined rate is 1/6. in order to find y's rate let's subtract 1/9 (x's rate) from 1/6 (x's and y's combined rate)

1/6 - 1/9 = 1/18. 1/18 is y's rate. the prob asks: How many hours would it have taken machine y working alone to complete the entire job? so, 1/18t=2/3 ==> t=36/3 = 12.

What do you all think? Any probs w/this?
Re: work question   [#permalink] 01 Jun 2007, 16:09
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