Answer
The total time for driving and hiking is $T\left( x \right)=\frac{10}{x}+\frac{5}{x}$
Work Step by Step
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 $T\left( x \right)=\frac{10}{x}+\frac{5}{x}$.
