A rubber band is 1 meter long. An ant starts at one end, crawling at 1 millimeter per second. At the end of each second, the rubber band is instantaneously stretched by an additional meter. (So, at the end of the nth second, the rubber band becomes n+1 meters long.)

Does the ant ever reach the far end of the band? If so, when?

We first must realise that a rubber band in this case is presumed to be oval, thus no end. So for the ant to reach the end, the rubber band must break. Which leads into the next assumption that the ant does not fall off the rubber band when it breaks. Having found data from www.chemheritage.org/EducationalServices/ faces/teacher/poly/activity/feat.htm , whichs shows in an experiment that a 10cm long rubber band breaks at 58.9 cm, I make the assumption that a 1 metre long rubber band breaks at 5.89 metres.

Next; the lifespan of an "ant", roughly maxuimum being hammer.prohosting.com/~penz/encycl/lifespan.htm <
An ant can live up to 5 years, so

The rubber band will break at 5.89 meters and at 1 millimetre per second will take the ant 5890 seconds or 98 minutes and 10 seconds to reach the end of "he" doesn't fall off. The lifespan of an ant being 5 years, I say yes the ant reaches the end of the rubberband. :-)

Posted by gavin on 2003-03-31 02:47:39