Answer
Car $50\ mph$, bus $30\ mph$.
Work Step by Step
Step 1. Assume the average velocity of the car is $x$ miles per hour; then the average velocity of the bus is $x-20$ miles per hour.
Step 2. For the same amount of time $t$, we have $t=\frac{300}{x}=\frac{180}{x-20}$, which gives $\frac{5}{x}=\frac{3}{x-20}$
Step 3. Cross multiply the above equation to get $5x-100=3x$. Thus we have $x=50\ mph$ and $x-20=30\ mph$.
