Problem of the Fortnight #14

A certain table has the shape of a regular pentagon, and each side of the pentagon measures 24 inches. One hundred and twenty five ants are simultaneously placed on top of the table. Immediately, each ant starts to walk in a straight line at a rate of one inch per second until either it falls off the edge of the table or until it collides head-on with another ant, in which case they both instantaneously turn around and continue to run in the opposite direction. What is the longest time one may have to wait before all the ants have fallen off the table?

(We are assuming that these ants’ anatomy is so peculiar that when their paths intersect at any other angle, they go through each other!)

Solutions are due by 4:30 PM on Friday, April 27.

Click here for previous problems (with solutions when available):