Will The Ant Reach The End?
An ant is crawling at a rate of along a rubber band which can be stretched uniformly. Suppose the rubber band is initially one meter long and it is stretched an additional meter at the end of each minute. If the ant begins at one end of the band, will it reach the other end?
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
Minute after minute, the ant walks relatively to the changing length of the rubber a part that is 1 0 1 + 1 1 1 + 1 2 1 + . . . which goes to infinity. So it will give sometime a value bigger than 1, which means the ant will meet the end of the rubber (and that is true whatever the initial length of the rubber is).
With initial length of 10 cm, it would be at the end after a time between 16 and 17 minutes.
If the ant walks n 1 of the length of the rubber during the first minute, it will take about n ( e − 1 ) minutes to get to the end.