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# Six machines, each working at the same constant rate

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Intern
Joined: 05 Sep 2016
Posts: 9
Re: Six machines, each working at the same constant rate [#permalink]

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04 Dec 2016, 02:34
if 6 machines do the job in 12 hours, then the ratio is 6:12.
if we want to do the same job in 8 hours, then 12 need to be multiplied by 2/3, 12 * 2/3 = 8.
Thus, since work and time are reciprocal, 6 machines have to be multiplied by 3/2, then 6 * 3/2 = 9.
Intern
Joined: 13 Dec 2016
Posts: 45
Re: Six machines, each working at the same constant rate [#permalink]

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20 Jan 2017, 02:06
A simple way to solve this problem is to form an equation based on inverse proportion :
If 6 machines take 12 days to complete the job, logic says that more machines will be needed to do the same job in less no. of days (here 8 days).
Let x be the additional machines needed to complete the job in 8 days.
Hence, our equation will be:
6/ (6+x) = 8/12
Solve it for x to get 3 as the answer
Intern
Joined: 24 Sep 2016
Posts: 37
Location: United States (CT)
GPA: 3.81
WE: Analyst (Venture Capital)
Re: Six machines, each working at the same constant rate [#permalink]

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20 Feb 2017, 17:35
Six machines to complete a job in 12 days means that every day each machine completes 1/72 of the job. So to complete a job in 8 days it would take 9 machines since 9 machines complete 9/72 of the job a day. Multiplied by 8 it will take those 9 machines 8 days to complete 72/72 percent of the job which is 100%.
Manager
Joined: 03 Jan 2017
Posts: 184
Re: Six machines, each working at the same constant rate [#permalink]

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28 Mar 2017, 11:00
speed time work
6 machines 6x 12 1
? ? 8 1

As we know that machiens do the same work, we can say x=1, then they do 72, 72/8=9, 9-6=3 answer is 3
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Joined: 27 Dec 2016
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Concentration: Social Entrepreneurship, Nonprofit
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Six machines, each working at the same constant rate [#permalink]

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22 Apr 2017, 15:47
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a 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

Solution :

1. 1/12 = 6 X $$\frac{1}{X}$$, thus we get X = 72.

2. $$\frac{6}{X}$$ + ( y X $$\frac{1}{X}$$ ) = 1/8, plugging X value = 72; thus we get y = 6

3. Difference between 2 value is the answer, thus = 3.
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Re: Six machines, each working at the same constant rate [#permalink]

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07 Apr 2018, 10:40
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.

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B

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Intern
Joined: 14 Feb 2016
Posts: 37
Re: Six machines, each working at the same constant rate [#permalink]

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18 Apr 2018, 07:04
1) Find the total ‘days of work’ with 6 machines: 12*6 = 72.
2) Find the total amount of machines required 72 days of work, in 8 days. 72/8.
3) We find that 9 machines are required for 72 days of work.
4) This means we need 3 additional machines. Answer choice is B.
Intern
Joined: 01 Apr 2018
Posts: 9
Re: Six machines, each working at the same constant rate [#permalink]

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18 Apr 2018, 07:12
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a 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

Total work done = 12*6=72 unit
Same work to be done by let n machine in 8 days :
8*n=72 or n=9 machine
Hence extra machine require =9-6=3 nos

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Re: Six machines, each working at the same constant rate   [#permalink] 18 Apr 2018, 07:12

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