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Working alone at it's own constant rate, a machine seals K

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Working alone at it's own constant rate, a machine seals K [#permalink] New post 03 Jan 2006, 18:45
Working alone at it's own constant rate, a machine seals K cartons in 8 hours, and working alone at it's own constant rate, another machine seals K cartons in 4 hours. If the two machines, each working alone at it's own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

A) 25%
B) 33 and 1/3%
C) 50%
D) 66 and 2/3%
E) 75%
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Re: Work Question [#permalink] New post 03 Jan 2006, 19:42
ellisje22 wrote:
Working alone at it's own constant rate, a machine seals K cartons in 8 hours, and working alone at it's own constant rate, another machine seals K cartons in 4 hours. If the two machines, each working alone at it's own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

D) 66 and 2/3%

D. faster machine can do k in 4 hours
faster machine can do 2k in 8 hours
slower machine can do k in 8 hours
(faster + slower) machine can do (2k+k) in 8 hours

% of cartoons faster machine does = 2k/3k=2/3 of total or 67%
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 [#permalink] New post 03 Jan 2006, 22:21
In 1 hr Machine A does k/8 cartons
In 1 hr Machine B does k/4 cartons (B is faster)

Lets dsay both worked for time t
means kt/8(A) +kt/4(B)=3kt/8 (total cartons)
What are we asked

Carton done by B/Total cartons =(kt/4)/(3kt/8)*100= 200/3=66 and 1/3%
  [#permalink] 03 Jan 2006, 22:21
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