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Working alone at its own constant rate, a machine seals k

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Manager
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Working alone at its own constant rate, a machine seals k [#permalink] New post 28 May 2006, 18:52
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1.Working alone at its own constant rate, a machine seals k cartons in 8hrs, and working alone at its own constant rate, a second machine seals k cartons in 4hrs. If the two machines, each working at its 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)33.33%
C)50%
D)66.66%
E)75%


2.A certain business produced x rakes each month from November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage cost of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes fro the 12 months from November through October?

A)0.40x
B)1.20x
C)1.40x
D)1.60x
E)3.20x

Please include explanations...
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 [#permalink] New post 28 May 2006, 19:29
q1:
plug in some numbers
say Say k =40

1st machine 40 cartons in 8 hours
= 20 cartons in 4 hours

2nd machine 40 cartons in 4 hours

Both machines 60 cartons in 4hours
percent of the cartons were sealed by the machine working at the faster rate?
40/(40+20) * 100

=66.66%
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 [#permalink] New post 28 May 2006, 20:35
Machine A --> seal k cartons in 8 hours; 1 hour seal k/8 cartons
Machine B --> seal k cartons in 4 hours; 1 hour seal k/4 cartons

Together, they seal 3k/8 cartons in 1 hour.
% sealed by the faster machine = (k/4)/(3k/8) * 100 = (k/4)(8/3k)*100 = 66.67%
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 [#permalink] New post 28 May 2006, 20:40
Nov - Feb --> 4 months. Each month produce x rakes.
Mar - Oct --> 8 months. Each month ship x/2 rakes.

Total rakes produces = 4x
March --3.5x(0.1)
April --3x(0.1)
May -- 2.5x(0.1)
June -- 2x(0.1)
July -- 1.5x(0.1)
Aug -- 1x(0.1)
Sep -- 0.5x(0.1)
Oct -- No charge

Total = 0.1x(3.5+3+2.5+2+1.5+1+0.5) = 1.4x
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 [#permalink] New post 29 May 2006, 07:14
OA:
question 1: 66.66%
question 2: 1.40x

ywilfred,
Thanks for all the explanations. You are very good. I looked at it and looked at it and could not make heads or tails... :oops:
  [#permalink] 29 May 2006, 07:14
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