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Re: A group of 8 machines that work at the same constant rate ca [#permalink]
1
Carcass wrote:
A group of 8 machines that work at the same constant rate can complete 14 jobs in 7 hours. How many hours would it take 17 of these machines to complete 34 of these jobs?

A. 4

B. 6

C. 8

D. 12

E. 16



First, let's find out how much 1 machine can do in 1 hour.

\(\frac{jobs}{hour}\) = \(\frac{14jobs}{7hours}\) = \(\frac{2jobs}{hour}\)

So in 1 hour, all 8 machines complete 2 jobs.

How much of the job can 1 machine do in 1 hour?

\(\frac{job}{machine}\) = \(\frac{2}{8}\) = \(\frac{0.25}{1}\)

So in 1 hour, 1 machine completes \(\frac{1}{4}\) of the job.

To illustrate this:

Machine 1: 1/4
Machine 2: 1/4
.
.
Machine 8: 1/4

(1/4)*8 = 2 jobs after 1 hour.


Now we have 17 machines, all of them doing \(\frac{1}{4}\) of the job per hour. So how many hours would it take to complete 34 jobs?

\(\frac{1}{4}* 17 = \frac{17}{4}\) after one hour

\(\frac{1}{4}* 17 = \frac{17}{4}\) after two hours, so \(\frac{17}{4}+\frac{17}{4} = \frac{34}{4}\) of the job is complete.
.
.
.

What we'd do is let \(x\) be the amount of time taken to complete 34 jobs:

\(\frac{17}{4} * x = 34\)

\(\frac{1}{4} * x = 2\)

\(x = 8\)

Giving C as the answer.
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Re: A group of 8 machines that work at the same constant rate ca [#permalink]
All relationships are directly proportional and we cross multiply in directly proportional relationship.
Machines:Jobs:Time
8:14:7
17:34:x

More machines can do more jobs so 8 *34 and 17*14
More jobs will take more time so 34*7 and 14*x

Combine all of them
8*34*7 = 17*14*x
x=8 option C
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Re: A group of 8 machines that work at the same constant rate ca [#permalink]
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