Answer
Passenger train $60$ miles per hour; freight train $40$ miles per hour.
Work Step by Step
Step 1. Assume the average velocity of the passenger train is $x$ miles per hour; then the average velocity of the freight train is $x-20$ miles per hour.
Step 2. For the same time $t$, we have $t=\frac{240}{x}=\frac{160}{x-20}$, which gives $\frac{3}{x}=\frac{2}{x-20}$.
Step 3. Cross multiply for the above equation to get $3x-60=2x$. Thus we have $x=60\ mph$ and $x-20=40\ mph$.
