A hare runs a twomile race with a tortoise The tortoise has

A hare runs a two-mile race with a tortoise. The tortoise has a one-mile head start. Even though the hare runs ten times faster than the tortoise, it seems unable to catch up for the following reason: When the hare gets to the spot where the tortoise started, the tortoise is one-tenth of a mile farther on; when the hare gets to this one and one-tenth-mile point, the tortoise has moved on from it and is still ahead; and so on. Explain this seeming paradox

Solution

There is no paradox. Seems like a paradox because we are also looking at smaller and smaller time intervals. The intervals considered in this \'paradox\' tend to 0 which is why hare doesn\'t seem to catch up.

In reality as the tortoise travels 1/10 mile hare has travelled a mile.

As the tortoise travels the next 1/10 mile the hare would have finished the race