Subject: Sunrise Problem: V. Arnold's first eureka! experience

Vladimir Arnol'd mentioned the following problem in a recent Notices 
interview.  Can you solve this problem as elegantly as did the budding 
great mathematician?

  The first real mathematical experience I had was when our schoolteacher 
  I. V. Morozkin gave us the following problem:  Two old women started at 
  sunrise and each walked at a constant velocity.  One went from A to B 
  and the other from B to A. They met at noon and, continuing with no stop, 
  arrived respectively at B at 4 p.m. and at A at 9 p.m.  At what time was 
  the sunrise on this day?

  I spent a whole day thinking on this oldie, and the solution (based on
  what is now called scaling arguments, dimensional analysis, or toric
  variety theory, depending on your taste) came as a revelation.  The
  feeling of discovery that I had then (1949) was exactly the same as
  in all the subsequent much more serious problems--be it the discovery 
  of the relation between algebraic geometry of real plane curves and
  four-dimensional topology (1970) or between singularities of caustics
  and of wave fronts and simple Lie algebra and Coxeter groups (1972).
  It is the greed to experience such a wonderful feeling more and more
  times that was, and still is, my main motivation in mathematics.

  -Vladimir Arnol'd, in  http://www.ams.org/notices/199704/arnold.html

-Bill Dubuque