Two peasant ladies go to the market

It looks like nobody wants to be the first one to publish a post!

I’ll do, but the first post won’t be mine either. This is a problem I read somewhere in a book or article by V. I. Arnol’d.

Two peasant ladies leave simultaneously at dawn because they are going to a farmers’ country market: one lady leaves from town A and is going to B, while the other one is on her way from B to A. They walk at constant speed (each one at her own speed). At midday sharp, they greet each others without stopping and continue on their way.

At 16 (that is, 4 p.m.) the faster lady reaches her destination, and at 21 the other lady arrives, too.

Compute sunrise time.


Credits and source attribution

You can read Arnol’d telling the story at this link:
http://www.ams.org/notices/199704/arnold.pdf

Let us quote a few lines for our readers.

“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.”

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