Six machines, each working at the same constant rate

Question

Six machines, each working at the same constant rate, together can complete a certain job in 12 days.
How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?

a.2
b.3
c.4
d.6
e.8

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3

Source: GMAT Prep

A. 2
B. 3
C. 4
D. 6
E. 8

Bunuel · Accepted Answer

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days? 
A. 2 
B. 3 
C. 4 
D. 6 
E. 8

Say a single machine requires x days to complete the job. Hence, the rate of one machine is 1/x job/day, (as the rate is reciprocal of time). Consequently, the combined rate for six machines is 6/x.

Using the equation 'work = time*rate', we have 1 = 12*6/x, which simplifies to x = 72 days. Therefore, a single machine would take 72 days to complete the task.

To finish the task in 8 days, 72/8 = 9 machines are needed.

The difference is thus 9 - 6 = 3 machines.

Answer: B.

Alternatively, we can consider it like this: we want to reduce the completion time from 12 days to 8, which is 2/3 of the original time. Consequently, we need to increase the work rate to 3/2 of the original rate. This implies we need 6*3/2 = 9 machines in total. Therefore, an additional 3 machines are required.

LalaB · Answer

6 machines in 12 hours can make 6*12=72 units.
x machines in 8 hours can make x*8=72 units x=9

12-9=3 more machines are needed
hope it helps

Bunuel · Answer

17. Work/Rate Problems 
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On other subjects:
 ALL YOU NEED FOR QUANT ! ! ! 
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amitdesai16 · Answer

Actually, this was more simple than I thought. When I first saw this, I started to panic thinking it's a rate question. But then I took a step back, and it was the simplest of calculations.

So here's the deal:

12 days -> 6 machines: 8 days -> ?

8 days means you definitely need more machines than the 6 and in such case the equation looks like-

12 * 6 = 8 * x

Therefore, x = 72 / 8 = 9

So 9-6=3 more machines

bangalorian2000 · Answer

let each machine work at rate of x days
1/x+1/x+1/x+1/x+1/x+1/x = 1/12
6/x = 1/12
x = 72
now y is number of machines needed to complete job in 8 days so,
y/72 = 1/8
y = 9
required = y-x = 3 hence b.

Silvers · Answer

Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.

So 3/2* 6 = 9

So we need 9-6 = 3 more machines.

dimitri92 · Answer

6 machines require 12 days = 72 machine days
how many machines to do the job in 8 days =  \frac{72 machine-days}{8 days} = 9 machines

so, 3 more machines.

gmatfighter12 · Answer

This is how I did it

6 machines in 1hr do 1/12 job
in 1 hr, 1 machine do 1/(12*6) job
In 8 days 1 machine do 8/(12*6)=1/9

Thus there is a need of 9 machine.

But I forgot to minus and get the difference so still get this question wrong.

mbaiseasy · Answer

Rate of machine = \frac{1}{m}

Draw the equation for 6 machines take 12 days:
 \frac{6}{m}=\frac{1}{12} 
 m=72 days

Let's look for the number of machines to work for 8 days:
 \frac{N}{72}=\frac{1}{8} 
 N=\frac{72}{8}=9 machines

Answer: 9 - 6 machines = 3 machines more

B

kabilank87 · Answer

6 x 12 = (6+x) x 8

9 = 6+x

x=3

smyarga · Answer

You can solve this problem without any equations. Just to calculate the rate of 1 machine.

The rate of 1 machine is  \frac{1}{6*12}=\frac{1}{72}  part per day.

So, 1 machine in 8 days can do  \frac{8}{72}=\frac{1}{9} .

So, to finish the job in 8 days we need 9 machines. Therefore 3 additional machines are required.

The answer is B.

crackjack · Answer

Somehow, I found below method to be working for me - 
6 Machines in 12 Days do 1 Work i.e. in notation form
6M * 12D = 1W,
so 1M * 1D =   W
How many Machines in 8 Days will complete 1 Work? i.e.
xM * 8D =   W = 1W

Solving for x in   = 1, we get x = 9 i.e. 9 Machines in 8 Days will do 1 Work. So 9-6=3 Machines more are required.

Ans - B

Asifpirlo · Answer

Here, 6 × 1/X = 1/12 or, X=72 . 2nd case, n × 1/72 = 1/8 or, n = 9 . additional = 9-6 = 3

PareshGmat · Answer

6 Machines do  \frac{1}{12}  work in 1 day

We require  \frac{1}{8}  work to be done in 1 day

Multiplication factor = \frac{\frac{1}{8}}{\frac{1}{12}} = \frac{1}{8} * 12 = \frac{3}{2}

Additional machines required  = 6 * \frac{3}{2} - 6 = 9 - 6 = 3

Answer = B

LUC999 · Answer

Six Machines:combined rate=6x
Time=12
Let Job be J

6x*12=J

Let M be the number of machines required to complete job in 8 days
Then
Mx*8=J

6x*12=Mx*8

M=9

Additional=9-6=3

Is this approach correct??

EMPOWERgmatRichC · Answer

Hi All,

We're told that 6 machines, working at the same constant rate, can finish a job in 12 days. We're asked for the number of EXTRA machines will you need to finish the job in 8 days?

This type of question is easiest to solve if you convert the info into "work units" Here, we start with 6 machines working for 12 days. This equals (6)(12) = 72 machine-days of work to finish the job.

If we wanted to finish the job in 8 days, it would still take 72 machine-days of work, so we'd need 72/8 = 9 machines.

We already have 6 machines, so we need 3 MORE machines to get the job done in 8 days.

Final Answer:  B

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

ScottTargetTestPrep · Answer

We are given that six machines, each working at the same constant rate, together can complete a certain job in 12 days. Since rate = work/time and if we consider work as 1, the rate of the six machines is 1/12.
 
We need to determine how many additional machines, each working at the same constant rate, will be needed to complete the same job in 8 days. In other words we need to determine how many additional machines are needed to work at a rate of 1/8. Since each machine works at the same constant rate, we can use a proportion to first determine the number of machines needed to work at the rate of 1/8.
 
Our proportion is as follows: 6 machines is to a rate of 1/12 as x machines is to a rate of 1/8.
 
6/(1/12) = x/(1/8)
 
72 = 8x
 
x = 9
 
So we need 9 – 6 = 3 more machines.

Answer: B

CrackverbalGMAT · Answer

Solution:

We know M1D1 = M2D2

=> M1 = 6 , D1 = 12 ,D2 = 8

Using the values, D2 = 6*12/8

= 72/8

=9 machines

=>Additionally = 9-6

= 3 machines  (option b)

Devmitra Sen (GMAT SME)

Schachfreizeit · Answer

so if one machine would need 60 min, so 1/60 to get the job done, 6 machines would need 10 min, bc 6/60=1/10?
I don't understand the equation: 1=12*(6/x). Why does 12*(6/x) equals 1?

Six machines, each working at the same constant rate

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Six machines, each working at the same constant rate

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