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A furniture manufacturer has two machines, but only one can [#permalink]

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05 May 2009, 20:12

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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

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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

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.
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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

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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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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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

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.

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
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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)

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.
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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)

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.

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]

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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]

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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.

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