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

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Director
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Joined: 10 Feb 2006
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It takes machine A x hours to manufacture a deck of cards [#permalink] New post 28 Sep 2006, 16:19
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/ x2 + 1

100x – y/x2 + 1

100y – x3 – x /x2 + 1

100y – x2y – y /x2 + 1

100x/ x2 + 1
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 [#permalink] New post 28 Sep 2006, 17:14
It would be easier if you use () and ^ :wink:

B it is

A--> x
B--> 1/x

A working for y hrs= (1/x)y=y/x

Working Together for n time:
100=y/x+n(1/x+x)
100=y/x+n((1+x^2)/x)

Solving for n:
=(100x-y)/(1+x^2)
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 [#permalink] New post 28 Sep 2006, 20:54
  [#permalink] 28 Sep 2006, 20:54
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It takes machine A x hours to manufacture a deck of cards

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