Solution: If car A travels x kilometers per hour, the speed of car B is x- 12 kilometers per hour.

meet

The distance traveled by car B is (4.5+35/x)(x- 12).

The distance between East Station and West Station is 4.5 times.

According to the distance relationship between Party A and Party B when they meet

(4.5+35/x)(x- 12)+35=4.5x (when both sides of the equation are multiplied by x, it can be seen at a glance that the quadratic term can be eliminated, which is actually a linear equation with one variable), and simplification.

70x-54x=420，

16x=420

x=26.25