When logic and calculus collide

[KenWittlief]

well, the problem was stated in terms of humans running a footrace, not in terms of imaginary dots moving along perfectly straight, perfectly parallel lines.

As Rich pointed out, the runners do not have to start from a stand still. In sailing races, and in Nascar the racers are moving when the race begins. As long as you dont cross the starting line before the opening shot your speed is up to you. If you are moving towards the starting line before the race starts, your speed is not zero, and it may not be zero at any point during the race (from 'Go' to the finish line).

Also, runners cant possibly stay exactly on the perfect centerline of a race course, so one person will end up running a longer distance than the other, therefore he could run faster for the entire race, and still finish with a tie.

This problem being worded this way brings up an interesting point: the math we learn in college is based on linear systems, but in the real world almost nothing is linear. So while we try to make the math work out to the nth degree of accuracy and precision (the right answer), in the real world the best we can do with math is approximate the non-linear physical world.