@Spyros: I think that's right from a pure energy point of view: the energy needed to go from 100-110mph equals the energy to go from 0-45.8 mph.
I'm not sure how well the pure energy analogy works (drag, efficiency of engine, etc.), but there is an ideal speed for fuel efficiency cars, and it's not around 110mph :).
@Kaizyn: Thanks for the info. Yep, I like this particular proof compared to others because it focuses on the larger concepts, not just re-arrangement of area.