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Ps: Machine A & Machine B

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Director
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Ps: Machine A & Machine B [#permalink] New post 17 Jul 2007, 14:41
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A
B
C
D
E

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Question Stats:

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Two machines are sawing wood but due to space limitations only one machine can work at a time. Machine A is used for the first shift and the other machine for the second shift, while both work for half the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with the current work schedule?

a) 14
b) 13
c) 11
d) 9
e) 7

Pls. explain your answer.
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Re: Ps: Machine A & Machine B [#permalink] New post 17 Jul 2007, 19:09
GK_Gmat wrote:
Two machines are sawing wood but due to space limitations only one machine can work at a time. Machine A is used for the first shift and the other machine for the second shift, while both work for half the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with the current work schedule?

a) 14
b) 13
c) 11
d) 9
e) 7

Pls. explain your answer.


Do not understand the question yet :oops:
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 [#permalink] New post 17 Jul 2007, 19:24
i got aprox. 9 days

A machine 1/12 for 2 shifts (which is 1/24 per shift, and 1/16 per 1.5 shift)
B machine 1/15 for 2 shifts (which is 1/30 per shift, and 1/20 per 1.5 shift)

1/16 + 1/20 = 9/80 (9 jobs completed for every 80 days)

then each job takes about 9 days to complete (80/9)

(D)
Director
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Re: Ps: Machine A & Machine B [#permalink] New post 17 Jul 2007, 22:25
GK_Gmat wrote:
Two machines are sawing wood but due to space limitations only one machine can work at a time. Machine A is used for the first shift and the other machine for the second shift, while both work for half the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with the current work schedule?

a) 14
b) 13
c) 11
d) 9
e) 7

Pls. explain your answer.


A's rate = 1/12 in 2 shifts
B's rate = 1/15 in 2 shifts

A's rate = 1/24 in 1 shift
B's rate = 1/30 in 1 shift

A's rate = 1/18 in 1.5 shifts
B' rate = 1/22.5 in 1.5 shifts

1/18 = 5/90, 1/22.5 = 4/90

9/90(t)=w, t=10
b/w C and D
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 [#permalink] New post 19 Jul 2007, 22:44
cocosdreamland wrote:
i got aprox. 9 days

A machine 1/12 for 2 shifts (which is 1/24 per shift, and 1/16 per 1.5 shift)
B machine 1/15 for 2 shifts (which is 1/30 per shift, and 1/20 per 1.5 shift)

1/16 + 1/20 = 9/80 (9 jobs completed for every 80 days)

then each job takes about 9 days to complete (80/9)

(D)


OA is D. Thanks for this great expl.
Director
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Re: Ps: Machine A & Machine B [#permalink] New post 19 Jul 2007, 23:30
sumande wrote:
ggarr wrote:

A's rate = 1/12 in 2 shifts
B's rate = 1/15 in 2 shifts

A's rate = 1/24 in 1 shift
B's rate = 1/30 in 1 shift

A's rate = 1/18 in 1.5 shifts should be 1/16 (1/24 + 1/48)
B' rate = 1/22.5 in 1.5 shifts should be 1/20 (1/30 + 1/60)

1/18 = 5/90, 1/22.5 = 4/90

9/90(t)=w, t=10
b/w C and D


I am getting 90/8 as well.

Sumande, please explain why it should be (1/24 + 1/48) and (1/30 + 1/60)
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 [#permalink] New post 12 Dec 2007, 12:55
A takes 12 days to do all the work of 2 shifts

A only does 1.5 shifts on the current schedule. This is 3/4 of 2 shifts.
We need to know how long it would take to do 12 days of work in ¾ of the time
12 / (3/4) = 12 * (4/3) = 16 days

A’s real rate is 16 days or 1/16
B’s real rate is 20 days or 1/20
  [#permalink] 12 Dec 2007, 12:55
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