An Old Interesting Paradox

A paradox is a contradiction. Here is an old paradox

In a two boy race, one who runs slower is given a head start say of 10 meters. But how the one who runs faster can ever catch up with him. When the fast runner gets to the point where the slow runner started, the slow runner has moved ahead though by less than 10 meters. When the fast runner gets to this new position of the slow runner, he is ahead again by this time. In this way, the gap continues to narrow but always remains.

The reasoning here seems sound but it is against a very common real world experience. Anything that travels faster can bypass and get ahead of another that travels slower.

This paradox was proposed by a Greek Zeno of Elea (495BCE – 430BCE). It is well known by the name ‘Achilles and the tortoise’. Basic idea of the paradox is presented in differing ways by books and websites.

However, seeming validity of the argument would not effect applying mathematics to a situation like the one here.

If some of the variables are known, the exact time or distance when the two runners are together can be easily calculated using simple algebra.

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