Xavier and Yonette are waiting for their plane at an airport, when Xavier proposes a race:

"See that moving sidewalk? Why don't you run on it, and then when you reach the end turn back and run to where you started from? I meanwhile will run the same path, but right next to it rather than on it."

Yonette thought about it and said:

"But I don't see the point... We both run with the same speed, and it's the same distance. Sure, I will gain a bit on you while the sidewalk increases my speed, but then I will just lose the advantage while I'm running back and we will arrive at the same time."

Assuming Xavier and Yonette do run with the same speed, who will win the race?

Call Xavier's and Yonette's running speed x, the walkway speed w and the distance d.

Xaviers time is 2d/x which can be expressed as 2dx/x²

Yonette's time is d/(x+w) + d/(x-w) = [d(x-w) + d(y+w)]/(x² - w²) = 2dx/(x² - w²)

since x² - w² ≤ x², then 2dx/(x² - w²) ≥ 2dx/x², and Xavier wins

Michelson and Morely used this principle in their experimtnt to measure the speed and direction of the "ether" When the two light beams tied, their experiment failed, and Einstein considered the possibility that it had to fail because light did not act like slower phenomenon, an Relativity was born.

Posted by TomM on 2002-12-05 22:48:00