Question

During rush hour, Fernando can drive 20 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads. What is the formula and what do I use where.

Time in each case is the same.

distance=rate*time
20=(9+vf)*time

where vf is the velocity on the freeway.
15=vt*time or time= 15/vf

put that in the first equation for time, and solve for vf. You will most likely have a quadratic equation.