Question

Each month Leo makes copies of a budget report. when he uses both the large and small copier, the job takes 30 minutes. if the small copier is broken, the job takes him 50 minutes. how long will the job take if the large copier is broken?

Answer 1

This word problem focuses on the time required to finish a certain job. If the copier both work at the same time, the job takes about 30 minutes. If the small copier is broken, only the large copier works and takes about 50 minutes. We let x be the time used by the small copier if the large copier is broken. This is written in an algebraic equation as

`(1)/(50)+(1)/(x)=(1)/(30)`

Solve for x, we have

`\begin{gathered} (1)/(x)=(1)/(30)-(1)/(50) \\ (1)/(x)=(5-3)/(150) \\ ^{}(1)/(x)=(2)/(150) \\ (1)/(x)=(1)/(75) \\ x=75 \end{gathered}`

Hence, it takes 75 minutes to get the job done if the large copier is broken.