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11. An old machine requires three times as many hours to complete a job as
a new machine. When both machines work together, they require 9 hours
to complete a job. How many hours would it take the new machine to
finish the job operating alone?

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Answer:

Step-by-step explanation:

[tex]9(r_n+r_o)=1\\ \\ r_n+r_o=\frac{1}{9}\\ \\ r_o=\frac{r_n}{3}\\ \\ r_n+\frac{r_n}{3}=\frac{1}{9}\\ \\ \frac{4r}{3}=\frac{1}{9}\\ \\ 4r=\frac{1}{3}\\ \\ r=\frac{1}{12}\\ \\ \text{So working alone it would take the new machine 12 hours to finish the job.}[/tex]