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
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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.
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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.