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Three machines operating independently, simultaneously, and
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09 Oct 2013, 18:23
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74% (00:52) correct 26% (00:50) wrong based on 1068 sessions
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Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled? A. 6 B. 9 C. 12 D. 27 E. 48
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Re: Three machines operating independently, simultaneously, and
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12 Feb 2015, 11:55
Hi All, These type of "work" questions can be solved in a variety of ways (depending on how you want to do the math). Since we have 3 machines, each of which works for 36 hours to complete a job, we know that.... (3 machines)(36 hours each) = 108 machinehours are needed to complete the job. Since we're told that all the machines work at the same rate, adding a 4th machine is not going to be difficult to deal with. The 108 machinehours are still needed to complete the job, but now we have 4 machines doing work instead of 3... (108 machinehours)/(4 machines) = 27 hours. Since the original time was 36 hours and the "new" time is 27 hours, the difference is 9 hours. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: Three machines operating independently, simultaneously, and
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10 Oct 2013, 03:39
Hi,
all 3 machine works at same rate = 1/x
1/x + 1/x + 1/x = 1/36 3/x = 1/36 x = 108.
Fourth machine was used with same rate (1/x) Total Rate for 4 MAchines = 4/x =4/108 =1/27 is the over all rate of four machine So time is 1/Rate = 27 hrs
Question asked was "how many fewer hours of simultaneous operation could the production order be fulfilled" so 36  27 = 9 Hrs




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Re: Three machines operating independently, simultaneously, and
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10 Oct 2013, 00:33
If 3 Machines can do the work in 36 hr then 4 Machines can do the work in 3/4*36 = 27 Hrs. hence time saved will be 9hr option B is the correct answer
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Re: Three machines operating independently, simultaneously, and
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06 Feb 2014, 09:09
3 Machines 36 hr 1 Machines 108 hrs 4 machines 27 hrs
Now 3627=9 hrs fewer......B
Rgds Prasannajeet



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Re: Three machines operating independently, simultaneously, and
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07 Feb 2014, 20:37
3 > 36 4 > x Because they are inversely related, 4x = 3*36 => x = 27. 369 = 27.



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Re: Three machines operating independently, simultaneously, and
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17 Jul 2016, 11:48
kiseki wrote: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
A. 6 B. 9 C. 12 D. 27 E. 48 \(\frac{36}{3}=\) 12 hours (each machine take 12 hours) (3 machines * 12 hours) = (4 machines take x hours) 12 * 3 = 4 * X 36 = 4x 9 = x 4 machines will take 9 hours less to finish the same order Answer B
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Re: Three machines operating independently, simultaneously, and
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22 Jul 2017, 18:03
kiseki wrote: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
A. 6 B. 9 C. 12 D. 27 E. 48 Let C = the rate of one of the machines 3C = 1/36 C = 1/(36*3) Add one more machine to determine the net impact... 4C = 4/(36*3) = 1/(9+3) It would take 4 machines 27 hours to finish the job. 3627 = 9 hours.



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Re: Three machines operating independently, simultaneously, and
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07 Aug 2017, 08:27
Use inverse proportion concept to solve it quickly.
Initial number of machines=3 New Number of machines=4(after adding one more machine)
So number of machines increases by 1/3 of the initial number
Since time taken will be inversely proportional to the number of machines, therefore if number of machines increases by 1/3, time taken decrease by 1/4
1/4 of 36 = 9.
Therefore B



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Re: Three machines operating independently, simultaneously, and
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07 Aug 2017, 11:10
a usual approach for work rate problems
3 machines, same productivity rate do some work in 36 hours, so mount of work is 108 if 1 more machine with the same rate is added then:
108 = 4*x x = 27 Question asks "how many fewer hours" so we subtract 27 from initial 36 = 9



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Re: Three machines operating independently, simultaneously, and
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17 Oct 2018, 10:56
Attachment:
Screen Shot 20181018 at 12.23.32 AM.png [ 38.2 KiB  Viewed 2755 times ]
If time taken by 4 machines is 27 hrs Time taken by 3 machines is 36 hrs. Question asks: how many fewer hours of simultaneous operation could the production order be fulfilled? 3627 = 9 hrs Same work would take 9 fewer hours.
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Re: Three machines operating independently, simultaneously, and
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12 Nov 2018, 00:57
Easiest way:
4x30 = 5x x= 24
Fewer hours : 3627
Answer 9.



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Re: Three machines operating
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24 Nov 2018, 21:49
shrik wrote: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?
6 9 12 27 48 Total machine hours= 3 * 36 = 108 Now, no. of machines = 4 Total work hours will be same Therefore, work can be completed in hours = total hours/ no. of machines = 108/4 = 27 hours Answer choice (D) Posted from my mobile device



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Re: Three machines operating
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24 Nov 2018, 22:16
shrik wrote: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?
6 9 12 27 48 Total no. of working hours of all the 3 machines = 3 * 36 = 108 hours
We add one more machine, but work will remain the same,
So new working hours completed by each machine = 108/4 = 27 hours
We want to know the difference between hours used in first and the second attempt,
Therefore, 36  27 = 9 (B)Alternatively,
3 * 36 = Work  (I)
4 * X = Work (II)
Where X is no. of working hours when one machine is added.
From I and II,
3 * 36 = 4 * X
X = 27 hours
Difference = 36  27 = 9 hours (B)
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Three machines operating independently, simultaneously, and
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25 Nov 2018, 08:00
kiseki wrote: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
A. 6 B. 9 C. 12 D. 27 E. 48 since the amount of work completed is the same, weather it will be 4 or 6 machines, I made following equation total machines/ hours \(36*3 = 108\) \((36x)*4= 108\) \(1444x=108\) \(4x =36\) \(x = 9\) So 9 hours fewer



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Re: Three machines operating independently, simultaneously, and
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25 Nov 2018, 12:01
kiseki wrote: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?
A. 6 B. 9 C. 12 D. 27 E. 48
\(? = \left( {{\rm{time}}\,\,3\,\,{\rm{mach}}{\rm{.}}\,\,{\rm{together}}} \right)  \left( {{\rm{time}}\,\,4\,\,{\rm{mach}}{\rm{.}}\,\,{\rm{together}}} \right)\,\, = \,\,36\,\,  \,\,{?_{{\rm{temp}}}}\,\,\,\,\,\,\left[ {\rm{h}} \right]\) \({\rm{each}}\,\,{\rm{mach}}{\rm{.}}\,\,{\rm{alone}}\,\,\, \to \,\,\,3 \cdot 36\,\,{\rm{h}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{?_{{\rm{temp}}}}\,\, = \,\,\,{{3 \cdot 36} \over 4}\,\,{\rm{h}}\,\,{\rm{ = }}\,\,27\,{\rm{h}}\) \(? = 36  27 = \,\,9\,\,\,\left[ {\rm{h}} \right]\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
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