TITLE: On a schoolchild puzzle of V.I. Arnold (re: toric varieties)
QUESTION [33 upvotes]: When reading the interview with Vladimir Arnold in the April 1997 edition of the Notices, I came across the following anecdote.

Many Russian families have the
tradition of giving hundreds of such
problems to their children, and mine
was no exception. 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.

I found the solution in a rather straightfoward fashion, but I was curious as to the parenthetic remark. So, can anybody tell me (as a total outsider to algebraic geometry), what does this problem have to do with toric varieties?

REPLY [5 votes]: I think the problem cannot be solved because the sun rises at different times at A and B in general
(say A = Vladivostok and B = Moscow).  All what can be said is that (12-tA)(12-tB) = 4x9 = 36.
If by chance the sun rise times are identical then tA = tB = 6.
This is obtained by using the similitude of triangles in the space-time diagram.