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A furniture manufacturer has two machines, but only one can

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rtaha2412
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A furniture manufacturer has two machines, but only one can [#permalink] New post   07 Jan 2011, 11:33
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Machine A can complete a certain job in 12 days, working 2 full shifts per day, while Machine B can complete the same job in 15 days, also working 2 full shifts per day. If Machine A works during the first shift each day, Machine B works during the second shift, and both machines work half of the third shift, approximately how many days will it take for Machines A and B to complete the job under this work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

M06-21

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Bunuel
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A furniture manufacturer has two machines, but only one can [#permalink] New post   07 Jan 2011, 11:50
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Official Solution:

Machine A can complete a certain job in 12 days, working 2 full shifts per day, while Machine B can complete the same job in 15 days, also working 2 full shifts per day. If Machine A works during the first shift each day, Machine B works during the second shift, and both machines work half of the third shift, approximately how many days will it take for Machines A and B to complete the job under this work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

Machine A requires 12 days * 2 shifts = 24 shifts to complete the entire job;

Machine B requires 15 days * 2 shifts = 30 shifts to complete the entire job;

Each day, both machines work 1.5 shifts (\(\frac{3}{2}\) shifts). Together, in one day, they complete \(\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}\) of the whole job. Therefore, under the current work schedule, they will need approximately \(\frac{80}{9} \approx 9\) days to finish the entire job.

Answer: D­
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AleenBola
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A furniture manufacturer has two machines, but only one can [#permalink] New post   05 May 2024, 07:04
If Machine 1 does total work in 24 days and machine B does the same in 30 days. Then the work can be 120 (LCM)
Machine A's rate- 10
Machine B's rate- 8

In one day, 3 shifts, they do a total work of = 27

Hence total number of days taken by them= 4.4

Bunuel. Can you help me with this?

 
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post   06 May 2024, 01:17
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AleenBola wrote:
If Machine 1 does total work in 24 days and machine B does the same in 30 days. Then the work can be 120 (LCM)
Machine A's rate- 10
Machine B's rate- 8

In one day, 3 shifts, they do a total work of = 27

Hence total number of days taken by them= 4.4

Bunuel. Can you help me with this?

Machine A can complete a certain job in 12 days, working 2 full shifts per day, which means in one shift A does 120/(12*2) = 5 units of work, not 10.

Machine B can complete the same job in 15 days, also working 2 full shifts per day, which means in one shift B does 120/(15*2) = 4 units of work, not 8.

In one day, they work 1.5 shifts each, hence do 7.5 and 6 units of work respectively.

120/(7.5 + 6) = 8.8...

Hope this helps.­
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Re: A furniture manufacturer has two machines, but only one can [#permalink]
06 May 2024, 01:17
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