Three machines operating independently, simultaneously, and

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:

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

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

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

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

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

Rgds
Prasannajeet

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

\(\frac{36}{3}=\) 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

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.

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

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

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.

Easiest way:

4x30 = 5x
x= 24

Fewer hours : 36-27

Answer 9.

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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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)
_________________

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

\(? = \left( {{\rm{time}}\,\,3\,\,{\rm{mach}}{\rm{.}}\,\,{\rm{together}}} \right) - \left( {{\rm{time}}\,\,4\,\,{\rm{mach}}{\rm{.}}\,\,{\rm{together}}} \right)\,\, = \,\,36\,\, - \,\,{?_{{\rm{temp}}}}\,\,\,\,\,\,\left[ {\rm{h}} \right]\)

\({\rm{each}}\,\,{\rm{mach}}{\rm{.}}\,\,{\rm{alone}}\,\,\, \to \,\,\,3 \cdot 36\,\,{\rm{h}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{?_{{\rm{temp}}}}\,\, = \,\,\,{{3 \cdot 36} \over 4}\,\,{\rm{h}}\,\,{\rm{ = }}\,\,27\,{\rm{h}}\)

\(? = 36 - 27 = \,\,9\,\,\,\left[ {\rm{h}} \right]\)


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

Regards,
Fabio.
_________________

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)

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

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).

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)