Back to the robots problem

Here is the problem from my previous post.
Four robots are initially at the vertices of a unit square.  They start moving simultaneously with the same speed, each one keeping its direction to the right closest neighbor.  Where do they meet and what distance will each one cover to the meeting point?
The answer to the first question is obvious due to the symmetry of the problem - they meet at the center of the square.  In order to answer the second question we can introduce a rotating frame of reference. 

The origin is where the robot A is at the moment.  The axis x is always directed to the robot D, and the axis y is always directed to the robot B.  Due to the symmetry of the problem the robots will always be at the vertices of the shrinking square up to the moment they meet at the origin.  If we look at the motion of the robot B, it moves along the axis y from the point (0, 1) to the origin.  So it moves exactly one unit to the meeting point.  The same is true about distances for other robots due to the symmetry as mentioned before.

I have known this problem since, probably, age 14, but today I did a Google search and found a lot of sites talking about it.  So I was planning to discuss the same situation for different regular polygons but decided just to put a link to the site with the short and meaningful discussion.
http://www.cut-the-knot.org/Curriculum/Geometry/FourTurtles.shtml

On a different note, I asked my algebra students to solve the following problem.  

Two cars start moving towards each other from A and B respectively with speeds 60 mph and 40 mph. The
distance AB is 750 mi. What will be the distance between these cars 1 hour before they meet?

It took them a few minutes to realize how simple it is, and at the end the strongest students were a bit upset at themselves.