Zeno's paradox

Yet another lunch hour, and yet another pointless discussion. A couple of puzzles and tricky mathematics questions found their way to the table. I was introduced to a Mathematical puzzle, more of a paradox. I'll try and recreate it in my own words. It involves the classic old tale of The Hare and the Tortoise, as narrated by my friend. The story goes this way. A hare and a tortoise agree to a race but the hare concedes to the tortoise, the luxury of having an initial lead before the actual race start. When the race was about to start, the tortoise presents an option to the hare. It says "You would not be able to win the race anyway. You would take time to come up to the point where I currently am. And by that time I would have drifted further away. And again when you try to reach me, I would have gone some more distance. So theoretically, I am the winner of this race." The hare did see a logic here, and conceded the race. (Am wondering, was this the origin of the phrase hare-brained?) Obviously there has to be a loophole here. Dying to get back to my seat to google it out.

Here is what i found. The exact version is slightly different, though. Its strangely called the Achilles and the tortoise paradox of motion. Thus it goes. Theoretically, rather paradoxically it states that In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. Strange, according to this, there would not be any of those chilling come from behind victories in modern sport. I was not able to find any fallacy in the logic. The post gives the false assumptions made to support the paradox. All this sounds interesting? Have a read here.

http://en.wikipedia.org/wiki/Zeno's_paradoxes
http://en.wikipedia.org/wiki/Zeno%27s_paradox_solutions