79. Oncoming Trains. At Wurzltown station, an old lady, looking out the window, shouted:

- Conductor! How long is it from here to Madville?
- All trains take 5 hours in either direction, ma'am, - he replied.
- And how many trains will I meet on the way?

This absurd question puzzled the conductor, but he readily answered:

- Trains from Wurzltown to Madville and from Madville to Wurzltown depart at five minutes past one, five minutes past two, and so on, with an interval of exactly one hour.

The old lady made one of her fellow passengers in the compartment find the answer to her question.

So how many trains will she meet on the way?
79. Since the train travels for 5 hours, we will divide the journey into 5 equal intervals. When the lady departs from Wurzeltown, 4 oncoming trains are already en route, and the fifth one is just leaving the station. She will meet each of these 5 trains. When the lady has traveled \(\frac{1}{5}\) of the distance, a new oncoming train will depart from Madville, when she has traveled \(\frac{2}{5}\) of the distance - another one, \(\frac{3}{5}\) - another one, \(\frac{4}{5}\) - another one, and finally, when she arrives in Madville, another, the fifth, train will be just departing from there. If we assume, as we should, that
\footnotetext{
* The answer follows directly from the theorem of velocity addition in mechanics, and the author's solution is merely an explanation of this theorem for the specific case under consideration.
}
she does not meet the last train "on the way" or the one that arrived in Wurzeltown when her train departed from there, then on the way from Wurzeltown to Madville, the lady will meet 9 trains.