1Cademy - Solving a Work Application: Printing Presses

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Rational Equation

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Solving a Work Application: Printing Presses

Apply the problem-solving strategy for work applications to find how long it takes two printing presses to complete a job together. If Press #1 takes $6$ hours alone and Press #2 takes $12$ hours alone, let $t$ be the hours needed together. In $1$ hour, Press #1 completes $\frac{1}{6}$ of the job, Press #2 completes $\frac{1}{12}$ of the job, and together they complete $\frac{1}{t}$ of the job. The rational equation is: $\frac{1}{6} + \frac{1}{12} = \frac{1}{t}$ Multiply both sides by the LCD, $12t$ :

ight) = 12t \left(\frac{1}{t} ight)$$ Distribute and simplify: $$2t + t = 12$$ $$3t = 12$$ $$t = 4$$ When both presses are running together, it takes $$4$$ hours to complete the job.

Updated 2026-05-01

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OpenStax Intermediate Algebra

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