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It takes machine A x hours to manufacture a deck of cards

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Manager
Joined: 07 Feb 2007
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It takes machine A x hours to manufacture a deck of cards [#permalink]

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26 Aug 2007, 20:30
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

It takes machine A x hours to manufacture a deck of cards that machine B can manufacture in 1/x hours. If machine A operates alone for y hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously?

(100y – x)/(x^2 + 1)

(100x – y)/(x^2 + 1)

(100y – x^3 – x)(x^2 + 1)

(100y – x^2y – y)(x^2 + 1)

100x/(x^2 + 1)

Nice question that I came across. Thought of posting it here. Will post OA later.
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27 Aug 2007, 02:00
(1/x)*y + (1/x + x)*Z = 100

[(1 + x^2)/x]*Z = 100 - y/x = (100*x - y)/x

Z = [(100*x - y)/x] / [(1 + x^2)]/x

Z = (100*x - y) / 1 + x^2

P.S> The only thing that we need to understand here is that we should deal with how much work is done by each machine in 1 hour.
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Re: Work Rate problem [#permalink]

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27 Aug 2007, 16:19
abhi_ferrari wrote:
It takes machine A x hours to manufacture a deck of cards that machine B can manufacture in 1/x hours. If machine A operates alone for y hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously?

(100y – x)/(x^2 + 1)

(100x – y)/(x^2 + 1)

(100y – x^3 – x)(x^2 + 1)

(100y – x^2y – y)(x^2 + 1)

100x/(x^2 + 1)

Nice question that I came across. Thought of posting it here. Will post OA later.

I did VICs prolly not the quickest way since it took me bout 4min
A B ---> rates will equal A: 1/x B: x
R 1/x x
T x 1/x
D 1 1

For me I couldnt figure out how to do this w/ the variables so...

x=2
y=10hrs

A works for 10 hrs at rate of 1/2 (1 deck every 2hrs) so A makes 5 decks.

now B comes in and there is 95 decks remaining. Find the combined rate

1/x+x/1 or 1/2+2=5/2decks/2hrs. (total rate)

use T=D/R 95/5/2= 38hrs

Ok now is where it begins to take a long time... plug in x and y into the answer choices.

E doesnt work, D is ugly and will take awhile to compute w/ the numbers I chose (come back to this if you exhausted the rest of the answers), C doesnt work,

B works....

A doesnt work. I went w/ B since I was just bought to cross 4min
Re: Work Rate problem   [#permalink] 27 Aug 2007, 16:19
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It takes machine A x hours to manufacture a deck of cards

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