Frank Morgan's Math Chat May 20, 1999 ANSWER (Joe Shipman). The
most interesting question turns out to be: Which direction
provides the best chance of reaching the tracks in time to
intercept the train? The answer is: due north or due south. Of
course if the train is heading westward, you have no chance,
unless you can outrun a train. Your only hope is that the train
is heading a relatively small angle q north of east [or south of
east, you have to guess which]. In this case, due north gives
you the best chance. You will reach the track before the train
if the ratio of your speed to the train's speed is greater than
the sine of q. This is true for anyone, no matter how far east
of the toot. If you take some other direction to the track,
you'll travel farther than someone else heading due north to the
same spot, and thus need a greater velocity. Unfortunately, even
if the mathematician runs due north at 1/4 the speed of the
train, he has only about a 4% chance that the train is heading a
small enough amount no