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# Six machines, each working at the same constant rate

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Intern
Joined: 05 Sep 2016
Posts: 9

Kudos [?]: 1 [0], given: 148

Re: Six machines, each working at the same constant rate [#permalink]

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04 Dec 2016, 01:34
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.

Kudos [?]: 1 [0], given: 148

Intern
Joined: 13 Dec 2016
Posts: 45

Kudos [?]: 10 [0], given: 571

Re: Six machines, each working at the same constant rate [#permalink]

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20 Jan 2017, 01:06
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

Kudos [?]: 10 [0], given: 571

Intern
Joined: 23 Sep 2016
Posts: 38

Kudos [?]: 7 [0], given: 81

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, 16:35
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%.

Kudos [?]: 7 [0], given: 81

Manager
Joined: 03 Jan 2017
Posts: 194

Kudos [?]: 11 [0], given: 4

Re: Six machines, each working at the same constant rate [#permalink]

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28 Mar 2017, 10:00
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

Kudos [?]: 11 [0], given: 4

Manager
Joined: 27 Dec 2016
Posts: 232

Kudos [?]: 55 [0], given: 249

Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)
Six machines, each working at the same constant rate [#permalink]

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22 Apr 2017, 14:47
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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Kudos [?]: 55 [0], given: 249

Manager
Joined: 30 Apr 2013
Posts: 95

Kudos [?]: [0], given: 9

Re: Six machines, each working at the same constant rate [#permalink]

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18 Dec 2017, 02:07
Could we solve this problem by assuming numbers for work?

Kudos [?]: [0], given: 9

Re: Six machines, each working at the same constant rate   [#permalink] 18 Dec 2017, 02:07

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