If I am an outside observer measuring your position with a very long ruler and your time with my wristwatch, all while watching your dashboard clock, I have access to three numbers. (Your clock, my watch, your position on my long ruler.)

There are three ways to compare these numbers. If I compare my watch to your position down the ruler, I will obtain "classical speed." The behavior of this number is very confusing when it is high.

I may also compare your dashboard clock with my ruler position, or your dashboard clock with my watch. Both of these can lead to a "speed," in the sense of one number changing at a certian rate with respect to another.

If Vx is the rate of change of the ruler position with respect to your dashboard clock, and Vt is the rate of change of my wristwatch with respect to your dashboard clock, and c is the speed of light, then it turns out to be always true that c^2*Vt^2 - Vx^2 = c^2. If you graph this you will see that it is a hyperbola.

In the parent's example, the car situation would obey V(north)^2 + V(south)^2 = 100mph^2. If you graph that it is a circle, as it differs from the above by the minus sign.