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Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule? A. 14 B. 13 C. 11 D. 9 E. 7
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16 Sep 2014, 00:28
Official Solution:Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule? A. 14 B. 13 C. 11 D. 9 E. 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 (\(\frac{3}{2}\) shifts), and together, in one day, they are doing \(\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}\)th of the whole, thus with the current work schedule they'll need \(\frac{80}{9} \approx 9\) days to do the whole job. Answer: D
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18 Mar 2015, 16:16
I think this question is poor and not helpful. Where does it say in this question what the length of one shift is? 1 Shift could equal 4 days for instance....



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31 Mar 2015, 11:14
Hi,
I had a different approach to solve this problem that was incorrect, but I'm having a hard time understanding why my approach was wrong, and why the official solution works the way it does.
What I did:
Added the rates (1 job/24 shifts and 1 job/30 shifts) 1/24+1/30 = 5/120 +4/120 = 9/120 combined rate. I used the reciprocal (120 shifts/9 jobs) as the time and converted this to days using the logic that together both machines complete three shifts/day. With this logic I got the answer ~4 days, which is obviously wrong, but I am having difficulty wrapping my head around why. If someone could help me understand this, I would be super grateful.



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Re: M0621
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13 Jun 2015, 05:59
Bunuel wrote: Official Solution:
Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule?
A. 14 B. 13 C. 11 D. 9 E. 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 (\(\frac{3}{2}\) shifts), and together, in one day, they are doing \(\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}\)th of the whole, thus with the current work schedule they'll need \(\frac{80}{9} \approx 9\) days to do the whole job.
Answer: D Hello I understand your point up to the point that each machine will work 1.5 shifts in a day as per the question. But I am unable to grasp the last point that you made in the equation \(\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}\)th of the whole. Can you please explain that how you arrive at this equation. Thanks



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Re: M0621
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13 Jun 2015, 09:04
vik09 wrote: Bunuel wrote: Official Solution:
Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule?
A. 14 B. 13 C. 11 D. 9 E. 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 (\(\frac{3}{2}\) shifts), and together, in one day, they are doing \(\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}\)th of the whole, thus with the current work schedule they'll need \(\frac{80}{9} \approx 9\) days to do the whole job.
Answer: D Hello I understand your point up to the point that each machine will work 1.5 shifts in a day as per the question. But I am unable to grasp the last point that you made in the equation \(\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}\)th of the whole. Can you please explain that how you arrive at this equation. Thanks Sure. In one day Machine A works of \(\frac{3}{2}\) shifts, and since Machine A needs 24 shifts to do the whole job, then in one day Machine A does (3/2)/24th of the whole job. In one day Machine B works of \(\frac{3}{2}\) shifts, and since Machine B needs 30 shifts to do the whole job, then in one day Machine B does (3/2)/30th of the whole job. Together they do \(\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}\)th of the whole job. Hope it's clear.
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Re: M0621
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13 Jun 2015, 19:09
Hi,
Could you please clarify how did you get 1.5 shifts (3/2). Probably I am missing out something really silly.



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14 Jun 2015, 12:46
ppac wrote: Hi,
Could you please clarify how did you get 1.5 shifts (3/2). Probably I am missing out something really silly. 3/2 = 1.5. Or did you mean something else?
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15 Jun 2015, 04:07
Hi,
I understand 3/2=1.5. How did you deduce "In one day each machine works 1.5 shifts (3/2 shifts)"



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ppac wrote: Hi,
I understand 3/2=1.5. How did you deduce "In one day each machine works 1.5 shifts (3/2 shifts)" Each day machine A is working during the first shift (1 shift), machine B is working during the second shift (1 shift) and both machines A and B are working half of the third shift (0.5 shifts each). Therefore, each work for 1 + 0.5 shifts per day. Hope it's clear.
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Re: M0621
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15 Jun 2015, 04:13
Thanks heaps! I knew I was missing something!



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Bunuel wrote: Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule?
A. 14 B. 13 C. 11 D. 9 E. 7 Alternative approach. Machine A can do a job in 12 days * 2 shifts = 24 shifts. Machine B can do a job in 15 days * 2 shifts = 30 shifts. \(\frac{1}{24} + \frac{1}{30} + (\frac{1}{24} + \frac{1}{30})/2\); \(\frac{18}{240} + \frac{9}{240} = \frac{27}{240}\); \(\frac{240}{27} ≈ 9\)



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11 Jul 2016, 02:21
another straight approach:
rate=============time======work 2Sa=============12=======1 machine A working 2 shifts completes the job in 12 days. => 1/12=2Sa => Sa=1/24 2Sb=============15=======1 machine B working 2 shifts completes the job in 15 days. => 1/15=2Sb => Sb=1/30 Sa+Sb+.5*(Sa+Sb)==x========1
the combined rate will be Sa+Sb (each machine works for 1 shift) + .5Sa+.5Sb (each machine works half of the third shift)
x=240/27=80/9=approx less than 9



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11 Feb 2017, 03:16
bschool42 wrote: Hi,
I had a different approach to solve this problem that was incorrect, but I'm having a hard time understanding why my approach was wrong, and why the official solution works the way it does.
What I did:
Added the rates (1 job/24 shifts and 1 job/30 shifts) 1/24+1/30 = 5/120 +4/120 = 9/120 combined rate. I used the reciprocal (120 shifts/9 jobs) as the time and converted this to days using the logic that together both machines complete three shifts/day. With this logic I got the answer ~4 days, which is obviously wrong, but I am having difficulty wrapping my head around why. If someone could help me understand this, I would be super grateful. Hi, you would calculate the time, if the machines would only work one shift each day. Furthermore you made a calculation mistake: If the combined Rate is 9/120 it takes 120/9 days to finish one Job, so at about 13.333 Days ... Hope it helps



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Re: M0621
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24 Jun 2017, 02:33
I did it this way and kinda worked.
12 and 15 common factor is 120.
A=> 12 days x 2 shifts x 5 components=120 b=> 15 days x2 shifts x4 components =120
A and B working together,
1shift x 5n + 1shift x 4n + 1/2(5n+4n)=120
13.5n=120
n is approximately 8.88



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12 Sep 2018, 11:52
>> !!!
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06 Nov 2018, 23:17
A better way to solve this question is to take LCM of 24 and 30=120. It means 120 work to be done. A does 1/24 work each day=>5 work each shift B does 1/30 work each day=>4 work each shift. In third shift both work half of the time,so work done=2.5+2=4.5 work Total work done in a day=13.5 work.For doing 120 work,it will take 9 days approx.










