Question

select the correct answer.

mr. koger is making copies of the school literary magazine to distribute to students and faculty. he has access to two copy machines: an older machine and a new machine. if he used only the older machine, it would take 80 minutes longer than if he used only the new machine. if he used both machines, he would finish the job in 30 minutes.

when \\(m\\) is the number of minutes it would take to finish the job using only the new machine, the situation is modeled by this rational equation:
\\\frac{1}{m} + \frac{1}{m + 80} = \frac{1}{30}\\

how many minutes would it take to finish the job if mr. koger used only the new machine?

• 20 minutes
• 40 minutes
• 50 minutes
• 60 minutes

Explanation:

Clear fractions by multiplying by the least common denominator

$$ 30(m + 80) + 30m = m(m + 80) $$

Expand and simplify to form a quadratic equation

$$
LATEXBLOCK0
$$

Factor the quadratic equation and solve for positive m

$$
LATEXBLOCK1
$$

Answer:

• 20 minutes
• 40 minutes (Correct answer)
• 50 minutes
• 60 minutes