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# Three machines operating independently, simultaneously, and

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Re: Three machines operating independently, simultaneously, and [#permalink]
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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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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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Re: Three machines operating independently, simultaneously, and [#permalink]
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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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kiseki
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 [#permalink]
kiseki
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.
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Re: Three machines operating independently, simultaneously, and [#permalink]
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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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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Attachment:

Screen Shot 2018-10-18 at 12.23.32 AM.png [ 38.2 KiB | Viewed 62132 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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Re: Three machines operating independently, simultaneously, and [#permalink]
Easiest way:

4x30 = 5x
x= 24

Fewer hours : 36-27

Answer 9.
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Re: Three machines operating [#permalink]
shrik
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)

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Re: Three machines operating [#permalink]
shrik
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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kiseki
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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kiseki
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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Three machines operating independently, simultaneously, and [#permalink]
Lets assume we have 36 units of work to be completed by 3 machines.

Therefore, we have 36 units = Rate x 36 hours =====> Rate = 1 unit/hour

Since prompt said the rate is constant for each machine, rate for one machine will be 1/3 unit/hour

Therefore, rate for 4 machines = 4 x 1/3 = 4/3 units per/hour

The time it will take for the 4 machines to complete 36 units of work = 36 units x 3/4 hours/unit = 9 x 3 = 27 hours

Finally, the fewer hours it takes for 4 machines = 36 - 27 = 9 hours (Answer choice B)

kiseki
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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kiseki
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

3 machines can do a work in 36 hours.
1 machine can do a work in 36*3 = 108 hours.
4 machines can do a work in 108/4 = 27 hours.

So number of fewer hours taken when 4 machines works simultaneously = 36 - 27 = 9 hours.

Answer B
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Three machines operating independently, simultaneously, and [#permalink]
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kiseki
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
The easiest way to solve this is to simply pick an easy number for the size of the production order, which is not given and hence doesn't matter (in other words, the correct answer is the same regardless of the order size), and to then calculate the number of hours required in each scenario. Let's say it takes 36 hours to make 36 golf clubs, for example. 36/36 = 1 so we make 1 golf club per hour. However, there are 3 machines so we make 1/3 of a club per hour, per machine.

So, each machine makes 1 golf club every 3 hours, and we add an additional machine. Now we have 4 machines making 1/3 + 1/3 + 1/3 + 1/3 = 4/3 clubs per hour. w = rt, so w/r= t. Since we need to make 36 golf clubs, it will take us [ [(36)/(4/3)] = 27 hours with 4 machines. 36-27 = 9, so the answer is Choice B.

Another trick is to realize that 4 is 33.3% greater than 3, so if you divide 36 by 1.33 you get 27. Be careful not to reduce 36 by 33%, though, because that will give you a false answer (Choice C).

Originally posted by mcelroytutoring on 07 Jul 2019, 13:17.
Last edited by mcelroytutoring on 08 Jul 2019, 09:16, edited 4 times in total.
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Re: Three machines operating independently, simultaneously, and [#permalink]
kiseki
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

Read carefully: We need to find out "in how many fewer hours of simultaneous operation could the production order be fulfilled?"

The Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours.

Four machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 27 hours.

Hence 36-27=9 fewer hours (option B is the correct ans)
Re: Three machines operating independently, simultaneously, and [#permalink]
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