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# Three machines operating independently, simultaneously, and

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Intern
Joined: 24 Oct 2011
Posts: 5
Schools: Sloan '16 (M)
Three machines operating independently, simultaneously, and  [#permalink]

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09 Oct 2013, 18:23
4
35
00:00

Difficulty:

25% (medium)

Question Stats:

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  [#permalink]

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12 Feb 2015, 11:55
16
7
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 machine-hours 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 machine-hours are still needed to complete the job, but now we have 4 machines doing work instead of 3...

(108 machine-hours)/(4 machines) = 27 hours.

Since the original time was 36 hours and the "new" time is 27 hours, the difference is 9 hours.

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Joined: 30 May 2013
Posts: 158
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Concentration: Entrepreneurship, General Management
GPA: 3.82
Re: Three machines operating independently, simultaneously, and  [#permalink]

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10 Oct 2013, 03:39
10
7
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
##### General Discussion
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Re: Three machines operating independently, simultaneously, and  [#permalink]

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10 Oct 2013, 00:33
5
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  [#permalink]

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06 Feb 2014, 09:09
3
3 Machines 36 hr
1 Machines 108 hrs
4 machines 27 hrs

Now 36-27=9 hrs fewer......B

Rgds
Prasannajeet
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Joined: 01 Aug 2006
Posts: 33
Re: Three machines operating independently, simultaneously, and  [#permalink]

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07 Feb 2014, 20:37
1
1
3 -> 36
4 -> x
Because they are inversely related, 4x = 3*36 => x = 27.
36-9 = 27.
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Re: Three machines operating independently, simultaneously, and  [#permalink]

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17 Jul 2016, 11:48
1
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
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Re: Three machines operating independently, simultaneously, and  [#permalink]

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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.

36-27 = 9 hours.
Intern
Joined: 19 Jun 2017
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Re: Three machines operating independently, simultaneously, and  [#permalink]

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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  [#permalink]

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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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Joined: 24 Sep 2018
Posts: 138
Re: Three machines operating independently, simultaneously, and  [#permalink]

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17 Oct 2018, 10:56
Attachment:

Screen Shot 2018-10-18 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?
36-27 = 9 hrs
Same work would take 9 fewer hours.
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Joined: 28 Jun 2018
Posts: 66
Re: Three machines operating independently, simultaneously, and  [#permalink]

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12 Nov 2018, 00:57
Easiest way:

4x30 = 5x
x= 24

Fewer hours : 36-27

Manager
Joined: 01 Mar 2015
Posts: 76

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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

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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  [#permalink]

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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 $$36*3 = 108$$

$$(36-x)*4= 108$$

$$144-4x=108$$

$$4x =36$$

$$x = 9$$

So 9 hours fewer
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Re: Three machines operating independently, simultaneously, and  [#permalink]

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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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Re: Three machines operating independently, simultaneously, and &nbs [#permalink] 25 Nov 2018, 12:01
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