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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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It takes machine A x hours to manufacture a deck of cards [#permalink]

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05 Feb 2006, 21:53
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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?

a (100y â€“ x)/x2 + 1

b (100x â€“ y)/x2 + 1

c (100y â€“ x3 â€“ x)/x2 + 1

d (100y â€“ x2y â€“ y)/x2 + 1

e 100x/x2 + 1
VP
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05 Feb 2006, 22:00
b?

Rate of A = 1/x
Rate of B = x

Work done by A in y hrs = y*1/x
Let z be the time that both A & B operate and finally complete the job

Total work = Work done by A in yhrs + Work done by A&B in z

100 = y/x + z (1/x+x)

100x = y + z (1+x^2)

=> z = (100x-y)/(1+x^2)
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Manager
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06 Feb 2006, 09:33
100 = y/x + z (1/x+x)

Why is it y/x and not x/y?

Thanks.
Director
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06 Feb 2006, 09:57
A produces ONE deck in X hours. So in Y hours it will produce Y/X decks.
06 Feb 2006, 09:57
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