Originally posted by PBE6
As with every problem I propose, this may have been asked and answered on a previous post. Them's the breaks.
Four cock-a-roaches, two male and two female, are sitting on a table in a square formation like so:
Each cock-a-roach is facing the next one going counterclockwise around the figure, getting an eye-l ...[text shortened]... orgy takes place as soon as they meet (all cock-a-roaches are smoking roaches during the race).
The cock-a-roaches will always be in a square, so all we need to do is calculate the rate of change of the side length, as a function of that length.
Suppose the side length is x. Then 'after a short time' x^2 will change to (x-h)^2 + h^2, which in the limit as h -> 0 gives a rate of change of -2x, so d(x^2)/dt = -2x.
=> -1/2sqrt(x^2) * d(x^2)/dt = 1
=> -x = t + c
at t = 0, x = 1. So c = -1. Hence the cock-a-roaches meet at time 1.