Answer
$6\ mph$
Work Step by Step
Step 1. Assume the average velocity on the return trip is $x$ miles per hour. Then the average velocity to the campus is $x+9$.
Step 2. With the one way distance of 5 miles, the total time is given by $\frac{5}{x+9}+\frac{5}{x}=\frac{7}{6}$.
Step 3. Multiply $6x(x+9)$ on both sides of the above equation. We have $30x+30(x+9)=7x(x+9)$, $7x^2+63x=60x+270$ and $7x^2+3x-270=0$
Step 4. Factor the above equation as $(x-6)(7x+45)=0$. Discarding the negative solution, we have $x=6\ mph$.
