A CUTE MOTION PROBLEM

You are walking across a bridge whose length you do not know, but at a constant speed of 8 mph.
When you reach 3/8's of the way across the bridge a train whistle announces its approach.  The train
is also traveling at a constant speed.  It turns out that:

1.           If you continue walking to the far end of the bridge, you and the train will arrive there at the same instant
2.           If you instantly turn around and walk to the near end, i.e. the end closer to you, you will arrive at that end
   at the same instant the train arrives there.

How fast is the train traveling?  Of course the problem can be solved algebraically, although the solution is a
considerable bit of work.  However, if you are clever you can do this entirely in your head.

Note: This problem was taken from the Aug. 19, 2001 Parade section of the Sunday Salt Lake Tribune.