Three machines operating independently, simultaneously, and

Question

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

A. 6
B. 9
C. 12
D. 27
E. 48

EMPOWERgmatRichC · Accepted Answer

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.

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

rrsnathan · Answer

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

nishtil · Answer

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

prasannajeet · Answer

3 Machines 36 hr
1 Machines 108 hrs
4 machines 27 hrs

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

Rgds
Prasannajeet

shreyas · Answer

3 -> 36
4 -> x 
Because they are inversely related, 4x = 3*36 => x = 27.
36-9 = 27.

zxcvbnmas · Answer

\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

cbh · Answer

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

GMATYoda · Answer

Screen Shot 2018-10-18 at 12.23.32 AM.png 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.

dave13 · Answer

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

fskilnik · Answer

? = \left( {{m{time}}\,\,3\,\,{m{mach}}{m{.}}\,\,{m{together}}} ight) - \left( {{m{time}}\,\,4\,\,{m{mach}}{m{.}}\,\,{m{together}}} ight)\,\, = \,\,36\,\, - \,\,{?_{{m{temp}}}}\,\,\,\,\,\,\left

{m{each}}\,\,{m{mach}}{m{.}}\,\,{m{alone}}\,\,\, 	o \,\,\,3 \cdot 36\,\,{m{h}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{?_{{m{temp}}}}\,\, = \,\,\,{{3 \cdot 36} \over 4}\,\,{m{h}}\,\,{m{ = }}\,\,27\,{m{h}}

? = 36 - 27 = \,\,9\,\,\,\left

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

shashankism · Answer

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

mcelroytutoring · Answer

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   = 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).

sayan640 · Answer

Use unitary method...

Take total work = 1
3 machines take 36 hours to complete the entire work = 1
1 machine take 36 hours to complete = 1/3 work
1 machine take 1 hour to complete = 1/ 3 * 36
4 machines take 1 hour to complete = 4/3 *36

4 machines complete the work in = 3 * 36 / 4 = 27 hours

4 machines take (36 - 27)= 9 hours less to complete the work.

Please give me KUDO s if you liked my explanation.

ScottTargetTestPrep · Answer

If 3 machines working together take 36 hours to complete a job, then 1 machine by itself will take 3 times as long, or 3 x 36 = 108 hours to complete the same job. However, 4 machines working together will take ¼ as long, or ¼ x 108 = 27 hours to complete the job. Therefore, 1 additional machine (added to 3 machines) will save 36 - 27 = 9 hours.

Answer: B

CrackverbalGMAT · Answer

There are multiple approaches to solve this Question. Let’s try a simple approach.
Since it is given that each machine work at the same constant rate, we can assume that each machine will do 1 order in 1 hour.
No of orders done by 1 machine in 36 hours = 36 orders
Total no of orders done by 3 machines in 36 hours = 36* 3 orders
If we add one more machine, then there is a total of 4 machines
Time taken by 4 machines to do the same no of orders = 36*3/4 = 9* 3 = 27 hours.

So four machines working together can fulfill the orders in 9 hours less time.

Option B is the answer.

Thanks,
Clifin J Francis
GMAT SME

bumpbot · Answer

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