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# Ps: Machine A & Machine B

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Director
Joined: 09 Aug 2006
Posts: 766
Followers: 1

Kudos [?]: 68 [0], given: 0

Ps: Machine A & Machine B [#permalink]  17 Jul 2007, 14:41
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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

Manager
Joined: 07 Feb 2007
Posts: 212
Followers: 2

Kudos [?]: 8 [0], given: 0

Re: Ps: Machine A & Machine B [#permalink]  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

Do not understand the question yet
Intern
Joined: 06 Apr 2007
Posts: 22
Followers: 0

Kudos [?]: 1 [0], given: 0

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
Joined: 12 Jun 2006
Posts: 536
Followers: 1

Kudos [?]: 29 [0], given: 1

Re: Ps: Machine A & Machine B [#permalink]  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

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
Director
Joined: 09 Aug 2006
Posts: 766
Followers: 1

Kudos [?]: 68 [0], given: 0

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
Joined: 12 Jun 2006
Posts: 536
Followers: 1

Kudos [?]: 29 [0], given: 1

Re: Ps: Machine A & Machine B [#permalink]  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)
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 348 [0], given: 4

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
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# Ps: Machine A & Machine B

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