Wednesday, 7 April 2010

Zeno’s Paradox Revisited

Two runners, Mr Hare and Mr Tortoise, run a marathon. Mr Hare is faster and completes the course in, let's say, three hours, whereas Mr Tortoise takes six hours.

Each of them wears an identical GPS running watch, which samples the runner's location once every second and uses the information to calculate speed and distance travelled.

The marathon follows a typical street circuit and each of the two runners follows exactly the same path, without cutting any corners or taking any shortcuts.

The question is, at the end of the race, which of Mr Hare and Mr Tortoise is likely to have travelled the furthest distance according to his GPS watch?

If you have a solution, post it as a comment, showing your working. (Note there are no tricks in this, it's purely an issue of mathematics, or possibly physics.)

I'll be posting my solution after the Brighton Marathon on Sunday April 18th, for which you can still sponsor me at I hope that my time will lie somewhere between those of Messrs Tortoise and Hare.

1 comment:

  1. I've just made a lovely diagram demonstrating on a circular course with samples every 20 mins the 9 point path of the hare is considerably shorter than the 18 point path of the hare. But you can't attach images to comments.