## Precalculus (6th Edition) Blitzer

The total time for driving and hiking is $T\left( x \right)=\frac{10}{x}+\frac{5}{x}$
Consider the average velocity on the hike to be x. Then, the average velocity while driving is $9x$. The time taken on the hike when the average velocity is $x$ and the distance is $5$ miles is $\frac{5}{x}$. The time taken while driving when the velocity is $9x$ and the distance is $90$ miles is $\frac{90}{9x}$. Consider the total time for driving and hiking to be represented by $T\left( x \right)$ , where $x$ is the average velocity on the hike. The total time is represented by, \begin{align} & T\left( x \right)=\frac{90}{9x}+\frac{5}{x} \\ & =\frac{10}{x}+\frac{5}{x} \end{align} Therefore, the total time for driving and hiking is $T\left( x \right)=\frac{10}{x}+\frac{5}{x}$.