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A furniture manufacturer has two machines, but only one can

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A furniture manufacturer has two machines, but only one can [#permalink] New post 07 Jan 2011, 10:33
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A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working 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
[Reveal] Spoiler: OA
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Re: work rates [#permalink] New post 07 Jan 2011, 10:50
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A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?

14
13
11
9
7


Machine A needs 12 days * 2 shifts = 24 shifts to do the whole job;
Machine B needs 15 days * 2 shifts = 30 shifts to do the whole job;

In one day each machine works 1.5 shifts (3/2 shifts), doing (3/2)/24+(3/2)/30)=9/80 th of the whole job in one day, thus with the current work schedule they'll need 80/9=~9 days.

Answer: D.
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Re: work rates [#permalink] New post 26 Feb 2011, 17:02
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Bunuel.... please could you point out anymore questions of this type ? Thanks for all your help.
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Re: work rates [#permalink] New post 26 Feb 2011, 17:04
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 30 May 2013, 04:10
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 31 May 2013, 18:42
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rtaha2412 wrote:
A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working 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



Machine A: 12 days to complete task working two shifts -> 24 days working one shift -> 48 days working half shifts
Machine B: 15 days to complete task working two shifts -> 30 days working one shift -> 60 days working half shifts

In one day, each works 3 half shifts, so: 3 * (1/48 + 1/60) -> 1/16 + 1/20 = 9/80 of job per day, so ~ 9 days to complete total job.
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 01 Jun 2013, 00:04
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A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working 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


Let us look for LCM f 15 and 12. Say 60 is total work.
A completes in 12 days 2 shifts which means it works 2.5 hrs per shift. (60/12 = 5 hrs two shifts)
Similarly B completes in 15 days or works 2 hrs per shift.
Now, per day work as per shift plan 2.5 (A) + 2 (B) + (2.5 + 2)/2 (A and B combined) = 6.75 hrs per day
Total time = 60/6.75 which comes around 9 days.
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 22 Jun 2013, 14:49
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machine A finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts

Lets assume total work require 120 shifts

Therefore,
rate of A = 5 shifts/day
rate of B = 4 shifts/day
rate of (A+B) = 9 shifts/day

According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day

Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 26 Sep 2013, 00:31
Machines A & B work for 1.5 shifts a day.
So, in 2 days 3 shifts.(imagine 2 days=1 schedule)

A's production rate 12 days 2 shifts, so in 1 schedule rate is 8.
B's production rate 15 days 2 shifts, so in 1 schedule rate is 10

This implies: T=8*10/8+10 = 80/18 (for 1 schedule)
and we know 1 schedule is of 2 days,

(80/18)*2 = 9days (Approx)

Hence D. :)
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 20 Nov 2013, 09:41
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rtaha2412 wrote:
A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working 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


I actually got one of these right!!!!!!!!!!!!!!!! First time in about 80 attempts at a work rate problem! I'm so happy

So based on the info given, it takes 24 shifts for A to complete the job, and 30 shifts for B to complete the job, if they each worked independently. So the rate for A is 1/24 and for B 1/30. If each day they're working 1.5 shifts, then each day A completes 1.5/24 (which equals 1/16) and B is completing 1.5/30 (which equals 20). Finding a common denominator of 80, their total work per day combined is 9/80. Thus after working 1.5 shifts each per day for 9 days they'll have completed the whole job (8/9ths through the 9th day).
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 25 Dec 2013, 23:04
curious why some questions will specify an "approx" solution and provide rounded answer choices, others will not, however provide fractional answers (when applicable), and then others, such as above, will do neither/both? I understand the above job wasn't done until partly into the 8th day, so it did take 9 days to complete...

Bunuel, is a question such as the above fair game on the test? I have been under the impression that the answer choices will be exact, unless the question specifies an "approx" solution or the answer choices are based on objects that can't be physically split (people, cars, etc)...isn't a day an interval and/or unit of measure? thank you.
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 25 Dec 2013, 23:59
rtaha2412 wrote:
A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working 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


Let us say that the total work is of 240 units

A ---- 12 days ---- 2 shifts ----- 10 units per shift

B ---- 15 days ---- 2 shifts ----- 8 units per shift

When they work together A + B + (A+B)/2 = 10 + 8 + 9 = 27 units per shift

Every 3 shifts ---- 27 units
x 8 x 8

Every 24 shifts ---- 216 units

26 shifts ----- 216 + 18 = 234

In 27th shift the work will get finishe

1 Day ---- 3 shifts hence total days taken = 27/3 = 9 days

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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 26 Dec 2013, 00:46
rtaha2412 wrote:
A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working 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

The clause "while both work half of the third shift" is confusing. The phrase "each work half of the third phrase" would have had more clarity.
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 08 Jan 2014, 20:11
This question should have asked "approximately" how many days will it take for the machines to do the job.
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 08 Jan 2014, 21:17
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TooLong150 wrote:
This question should have asked "approximately" how many days will it take for the machines to do the job.


'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.

To finish a work say you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully.
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 08 Jan 2014, 22:26
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rtaha2412 wrote:
A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working 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



in one shift, A can do 1/24 of the work
in one shift, B can do 1/30 of the work
no of days required for the completion of the task by A and B together in the current schedule is (3/2)*((1/24)+(1/30))*t=1
t=8.888=9
Re: A furniture manufacturer has two machines, but only one can   [#permalink] 08 Jan 2014, 22:26
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