Math Help Forum: The Racetrack Principle

I'm not sure if you guys are familiar with this theorem. It is the racetrack principle by Jerry Uhl.

True/false? The racetrack principle can be used to justify the statement that if two horses start a race at the same time, the horse that wins must have been moving faster than the other throughout the race.

The word that gets me is "throughout". I don't know if that means overall as an average, or at every instantaneous moment.

Originally Posted by zintore

I'm not sure if you guys are familiar with this theorem. It is the racetrack principle by Jerry Uhl.

True/false? The racetrack principle can be used to justify the statement that if two horses start a race at the same time, the horse that wins must have been moving faster than the other throughout the race.

The word that gets me is "throughout". I don't know if that means overall as an average, or at every instantaneous moment.

You can certainly say this:

1. If a horse wins the race, it must have been moving faster than the other horse during some time interval of the race.

2. If, throughout the whole race, one horse is always faster than the other, the faster horse wins.

3. A horse can be moving faster than the other horse for some time interval of the race and still not win.

Originally Posted by zintore

I'm not sure if you guys are familiar with this theorem. It is the racetrack principle by Jerry Uhl.

True/false? The racetrack principle can be used to justify the statement that if two horses start a race at the same time, the horse that wins must have been moving faster than the other throughout the race.

The word that gets me is "throughout". I don't know if that means overall as an average, or at every instantaneous moment.

Discalimer: I am not familiar with this theorem I just looked it up in google.

I would say false, I think this question is just asking you if the converse of the racetrack principle is true. The theorem says that if one is travelling faster than the other at all times during the race, then it will win without a doubt. the term throughout means for all of the race, and it is not necessarily sure that the winning horse was always faster.

A good example in calculus would be the two functions. for

1
2

starting form x =0. 1 gets form to first however its gradients is not always more negative than 2.

Bobak