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 pm and at A at 9 pm.
At what time was the sunrise on this day?
Note: In the 1940's, school teacher I.V. Morozkin gave this old Russian problem to the young Vladimir Arnold, now a prominent Russian mathematician.
Source: S. Lui's "An Intgerview with Vladimir Arnold," Notices of the AMS, April 1997