Challenge #39 Result


V Alan White submitted a very interesting answer, as did many others. Here's the challenge and his solution..thanks Alan!

Charles' counterpart (mythical, thank goodness!) is walking across a train bridge. When he is three-eighths of the way across, he hears a train whistle behind him. Turning to look, he sees a train heading his way. Being a quick calculator, he immediately realizes that, should he return the way he came, the train will meet him at the edge of the bridge; yet, if he continues the other way, the train will catch up to him at the far edge of the bridge! All seems to be lost! Yet the man knows that he can run at a speed of eight miles per hour, and that a magical disappearance will save him if someone can deduce from this information the speed of the oncoming train! (WOW!) 

How fast is the train going? Please deduce the answer and rescue Charles' counterpart!!!!!



comments: There are two answers.  First and smart-ass-est, one cannot deduce the speed of any implied ONCOMING train, if by "oncoming" one means "coming from in front", for the train mentioned above is BEHIND the Chuck-counterpart.  Second, if we mean to deduce the speed of the train mentioned above, it must be 32 mph.  If Chuck-counterpart runs 3/8ths of the bridge's distance--in either direction--the train will be at the beginning of the bridge span.  So if Chuck-counterpart runs the 3/8ths in addition to the 3/8ths of the span already covered--6/8ths total--the train will be at the beginning of the span.  If the train will then coincide with Chuck-counterpart when he has run the remaining 2/8ths of the span, thus covering 8/8ths of the span in the time that Chuck-counterpart covers 2/8ths, then the train must be moving 4 times as fast as Chuck-counterpart (simple proportion of 8/8=2x/8).  Since Chuck-counterpart is moving at 8 mph, then the train must be moving at 32 mph.!
  Of course this assumes no accelerations are involved, so further assuming that the train has been moving throughout this scenario at constant velocity, Chuck-counterpart must either be capable of instantaneous running velocity, he was running at constant velocity throughout, or we must know his rate of acceleration to further refine the train's speed.  There's another hidden assumption to set up the scenario, by the way.  Either Chuck-counterpart has a Doppler-radar device to enable him to calculate that the train will meet him at the beginning of the span, or he is omniscient, in which case he knows that I have the right answer now anyway!