According to his interview to the Notices of the AMS, when Vladimir I. Arnold was 12 years old (in 1949) his teacher I.V. Morozkin, gave to his classroom (apparently 6th grade of a soviet primary school) the following question (see http://www.ams.org/notices/199704/arnold.pdf)
Two 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 that day?
My question is not how to solve this problem, but rather How to solve this problem using what 12 year old kids know (or knew during the soviet era).