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A furniture manufacturer has two machines, but only one can [#permalink]
05 May 2009, 20:12

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Question Stats:

56% (02:28) correct
43% (01:45) wrong based on 272 sessions

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?

Re: PS: Furniture Manufacturer [#permalink]
05 May 2009, 23:04

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priyankur_saha@ml.com 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?

14, 13, 11, 9, 7

Kindly explain it.

Given that in a day machine A works for 1.5 shifts and machine B works for 1.5 shifts.

A can complete the work in 12 days by working for 2 shifts So A working for 1.5 shifts will take 16 days to complete the work

B can complete the work in 15 days by working for 2 shifts So B working for 1.5 shifts will take 20 days to complete the work

So work done by A and B in one day = \frac{1}{16} + \frac{1}{20} = \frac{9}{80}

Hence the work will be completed on the 9th day.
_________________

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
25 Dec 2009, 03:42

can someone please explain how to arrive at 16 and 20 hours for machine A and B respectively, I'm very confused , the original explaination is not so clear at least to me

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
28 May 2010, 11:39

Machine A working 2 shifts finishes the job in 12 days , working 1.5 shifts time taken = 16 days Machine B working 2 shifts finishes the job in 15 days , working 1.5 shifts time taken = 20 days LCM of 16 & 20 = 80, considering total units to be completed as 80. Machine A completes 5 units a day , Machine B completes 4 units a day. Working together A&B complete 9 units a day, days taken to complete the job together = 80/9 ~8.88~9 days.
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Re: PS: Furniture Manufacturer (m06q21) [#permalink]
28 May 2010, 17:11

1/12 + 1/15 = 1/t....t = time working together t = 20/3 in 4 shifts (A and B each, utilize 2 shifts) Current rate = 3 shifts (A and B each, =1 and half shift) If 4 shifts = 20/3...then 3 shifts takes longer i.e 4/3 x 20/3 = 80/9 => 9th day (OA = D)
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Re: PS: Furniture Manufacturer (m06q21) [#permalink]
13 Jun 2010, 04:01

A working 2 shifts finishes the job in 12 days, working 1.5 shifts = 16 days B working 2 shifts finishes the job in 15 days , working 1.5 shifts = 20 days A & B both working 1.5 shift finishes the work in 80/9 days

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
18 May 2011, 22:49

Can someone please explain how to arrive at 16 and 20 hours for machine A and B respectively? I used the method suggested by acegre, but it is bit time consuming.

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
19 May 2011, 00:08

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This post received KUDOS

kannn wrote:

Can someone please explain how to arrive at 16 and 20 hours for machine A and B respectively? I used the method suggested by acegre, but it is bit time consuming.

Working 2 full shifts Vs. working 1.5 shift.

The time which is given in the question is for 2 full shifts per day. However, the machines work only 1.5 shifts everyday.

Let's say that every shift is of "x" hours.

If Machine A can do the job in 12 days working two shifts: 2 shifts = 2x hours per day 12 days = 24x hours Machine A needs 24x hours to complete the job.

Now, since A works only for 1.5 shifts: 1.5 shift = 1.5x hours 1.5x hours = 1.5 shift 1 hour = 1.5/(1.5x) shift [Unitary method] 1 hour = 1/x shift 24x hours = 24x/x shift = 24 shifts

1.5 shift = 1 day 1 shift = (1/1.5) day 24 shifts = 24/1.5 days = 16 days

Likewise, B: 2 Shifts = 2x hours per day 15 days = 30x hours B completes a task in 30x hours

Now, since B works only for 1.5 shifts: 1.5 shifts = 1.5x hours 1.5x hours = 1.5 shift 1 hour = 1/x shift 30x hours = 30x/x= 30 shifts

1.5 shifts = 1 day 1 shift = 1/1.5 days 30 shifts = 30/1.5 = 20 days.

****************************************

OR Simply,

2 times effort -> 12 days 1 time effort -> 12*2= 24 days 1.5 times effort -> 24/1.5 days

2 times effort -> 15 days 1 time effort -> 15*2= 30 days 1.5 times effort -> 30/1.5 days
_________________

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
19 May 2011, 00:18

Just rephrasing the question:

Machine A can do the job in 12 days working 2 full shifts and Machine B can do the job in 15 days working 2 full shifts. Machine A is utilized during the first shift and Machine B during the second shift, while both A and B work half of the third shift. How many days will it take to do the job with the current work schedule? (Consider 1 day has 3 shifts of equal period of time)

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
01 Jun 2011, 04:56

1

This post received KUDOS

Alternative method. If we rewrite the RTD question in terms of "shifts" it is easier to understand.

In terms of Shifts where there are 2 shifts/day: Rate x Shifts = Work 1/24 x 24 shifts = 1 1/30 x 30 shifts = 1

Now rewrite the eqs in terms of days, assuming one machine works the ENTIRE day: Rate x Days = Work 1/8 x 8 = 1 1/10 x 10 = 1

Since the shifts during a day is shared between A and B equally we know that the rate must be somewhere between 8 days and 10 days. Therefore the answer is 9.
_________________

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
07 Jun 2011, 20:07

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This post received KUDOS

hello everyone.. i was a bit confused with some of the answers but i finally had a eureka moment

Machine A - Calculation for 1.5 shift: 1 shift 24 days (12 days/ 0.5 = 24 days) 2 shifts 12 days 1.5 shift 16 days (24 days/ 1.5 = 16 days)

x amount of work is done in 16 days @ 1.5 shift

Machine B - Calculation for 1.5 shift: 1 shift 30 days (15 days/ 0.5 = 30 days) 2 shifts 15 days 1.5 shift 16 days (30 days/ 1.5 = 20 days)

x amount of work is done in 20

Conclusion:

x/16 + x/20 = x/y (x is the total amount of work needs to be done, y is the amount days required to complete the work for 1.5A+1.5B which is what we are solving for)

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
15 Dec 2011, 00:30

fluke wrote:

kannn wrote:

Can someone please explain how to arrive at 16 and 20 hours for machine A and B respectively? I used the method suggested by acegre, but it is bit time consuming.

Working 2 full shifts Vs. working 1.5 shift.

The time which is given in the question is for 2 full shifts per day. However, the machines work only 1.5 shifts everyday.

Let's say that every shift is of "x" hours.

If Machine A can do the job in 12 days working two shifts: 2 shifts = 2x hours per day 12 days = 24x hours Machine A needs 24x hours to complete the job.

Now, since A works only for 1.5 shifts: 1.5 shift = 1.5x hours 1.5x hours = 1.5 shift 1 hour = 1.5/(1.5x) shift [Unitary method] 1 hour = 1/x shift 24x hours = 24x/x shift = 24 shifts

1.5 shift = 1 day 1 shift = (1/1.5) day 24 shifts = 24/1.5 days = 16 days

Likewise, B: 2 Shifts = 2x hours per day 15 days = 30x hours B completes a task in 30x hours

Now, since B works only for 1.5 shifts: 1.5 shifts = 1.5x hours 1.5x hours = 1.5 shift 1 hour = 1/x shift 30x hours = 30x/x= 30 shifts

1.5 shifts = 1 day 1 shift = 1/1.5 days 30 shifts = 30/1.5 = 20 days.

****************************************

OR Simply,

2 times effort -> 12 days 1 time effort -> 12*2= 24 days 1.5 times effort -> 24/1.5 days

2 times effort -> 15 days 1 time effort -> 15*2= 30 days 1.5 times effort -> 30/1.5 days

Can someone please explain the highlighted region? Thanks.

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?

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), and together, in one day, they are doing (3/2)/24+(3/2)/30=9/80 th of the whole, thus with the current work schedule they'll need 80/9=~9 days to do the whole job.

Re: PS: Furniture Manufacturer (m06q21) [#permalink]
06 Jun 2012, 03:50

Its very simple. ...

Machine A- takes 12 days to complete the work, working 2 shifts. but we have to calulcate total days working 1.5 shifts Therefore, it will take 15 days to complete the work, working in 1.5 Shifts

Simlarly- Machine B takes 15 days......... working 2 Shifts therefore, it wil take 18.75 or 19 days to complete the work in 1.5 shifts

Re: A furniture manufacturer has two machines, but only one can [#permalink]
14 Jun 2012, 02:46

priyankur_saha@ml.com 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 works for 12 days in two shifts or 24 shifts, B works for 15 days in two shifts or 30 shifts.

Assuming 120 (LCM of (24,30)) units of total work is to be completed. So, in each shift work done by A = 120/24 = 5 units work done by A = 120/24 = 4 units

In 1.5 Shift A will complete 5*1.5 units of work = 7.5 units In 1.5 Shift B will complete 4*1.5 units of work = 6.0 units

So, in one day when A & B work together, they will complete 7.5+6= 13.5 units of work.

thus, total number of days in which they complete the work = 120/13.5=80/9 ~ 9 days

Re: A furniture manufacturer has two machines, but only one can [#permalink]
16 Jun 2012, 09:05

As explained by several others on this thread, the key to solving this type of rate problems is to standardise 'per given parameter' (in this case 'per shift')

Therefore machine A takes--> 12 days*1.5 shifts/2 shifts= 16 days (to work over 1.5 shifts) machine B takes----> 15 days*1.5 shifts/2 shifts= 16 days (to work over 1.5 shifts) Both working together do (1/16)+(1/20)=9/80 part of the job in one day. Therefore they finish in 80/9 days-->approx. 9 days.

Cheers
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Re: A furniture manufacturer has two machines, but only one can
[#permalink]
16 Jun 2012, 09:05