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Running at their respective constant rates, Machine X takes

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mpopatia
 Post subject: Running at their respective constant rates, Machine X takes
 Post Posted: Sat Jun 19, 2010 2:21 pm 
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Course Students


Posts: 1
Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if two machines together produce 5/4w 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

OA - E

I understand the OA method which uses algebra: 3(w/d + w/d+2) = 5/4w and solves to be 6, and then 2w = 12. However I attempted to use the RTW chart and got stuck! Is there a way to pick numbers for the variables and use the RTW chart for this type of problem?
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Viswanathan.harsha
 Post subject: Re: Running at their respective constant rates, Machine X takes
 Post Posted: Thu Jul 01, 2010 12:49 am 
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Posts: 43
Can you please work out the algebra for the given problem? I am having difficulty getting w=6. Is this problem from gmat prep?
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rash.patil
 Post subject: Re: Running at their respective constant rates, Machine X takes
 Post Posted: Thu Jul 01, 2010 4:53 am 
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Students


Posts: 4
Let T total number of days taken by machine X to produce W widgets.
Then Work done by x is 1 day is W/T

Work done by machine y in 1 day = W/(T - 2).

Combined work done in 3 days = 3( W/T + W/(t-2) )

= 3W( 2T-1 ) / (T- 2) which is equal to 5W/4
So equating the two equations we get

12( 2T - 1 ) = 5T( T - 2)
24T - 12 = 5T2 - 10T
5T2 - 32T + 12 = 0
(T-6) (5T+2) = 0.
Which gives T = 6.
So no. of days to produce 2W widgets = 2T = 12.
Ans: E
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Viswanathan.harsha
 Post subject: Re: Running at their respective constant rates, Machine X takes
 Post Posted: Fri Jul 02, 2010 3:32 am 
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Course Students


Posts: 43
I believe it is supposed to be 12 (2T-2)=5T(T-2)

This gives you 5T^2-34T+24=0

Giving you t=6
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mschwrtz
 Post subject: Re: Running at their respective constant rates, Machine X takes
 Post Posted: Mon Jul 12, 2010 11:31 pm 
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ManhattanGMAT Staff


Posts: 506
That's right Viswanathan.harsha
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