The Achilles and Turtle Paradox
Algebra
Level
2
Achilles is a Greek hero.
Let's say Achilles and a turtle decide to have a race. To make things fairer, Achilles gives the turtle a head start. Will Achilles ever reach the turtle?
Yes
No
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The answer is no because: in the time it takes Achilles to run the 500 meters head start - 50 seconds - the turtle will have crawled 25 meters. In the time Achilles will run those 25 meters - 2.5 seconds - the turtle will have crawled 1.25 meters. Achilles will pass this distance in about 0.1 second, but the turtle will have crawled 0.05 meters. As you can see, this can stretch on for infinity, up to thge smallest scale - the Planck Lenght.