Answer
The function that expresses the total time on the road trip is $T\left( x \right)=\frac{600}{x}+\frac{600}{x-10}$.
Work Step by Step
Consider the average velocity on the outgoing trip to be x.
Then, the average velocity on the return trip is $\left( x-10 \right)$.
The time taken on the outgoing trip when the velocity is $x$ and the distance is $600$ miles is $\frac{600}{x}$.
The time taken on the return trip when the velocity is $\left( x-10 \right)$ and the distance is $600$ miles is $\frac{600}{x-10}$.
Consider the total time on the road trip to be represented by $T\left( x \right)$ , where $x$ is the average velocity on the outgoing trip.
The total time is represented by,
$T\left( x \right)=\frac{600}{x}+\frac{600}{x-10}$
Therefore, the function that expresses the total time on the road trip is $T\left( x \right)=\frac{600}{x}+\frac{600}{x-10}$
