Jóska and Karcsi, during their excursion, come across a monument in the forest where a bus route runs. They decide to get on the bus. Jóska heads for the next stop, while Karcsi goes back to the previous stop, as he thinks it is closer. The bus reaches both of them at the same time. Was Karcsi right if he walks at $6 \mathrm{~km} / \mathrm{h}$, Jóska at $4 \mathrm{~km} / \mathrm{h}$, and the bus travels at $60 \mathrm{~km} / \mathrm{h}$?
Let the distance from the starting point to the bus stop towards which Karcsi is heading be denoted by $x$, and the distance to the other stop by $y$. Karcsi reaches the stop after $\frac{x}{6}$ hours. There, he immediately boards the bus and travels the entire distance between the two stops at a speed of $60 \mathrm{~km} / \mathrm{h}$, which takes another $\frac{x+y}{60}$ hours. Jóska can board the bus exactly $\frac{x}{6}+\frac{x+y}{60}$ hours later, which, according to the conditions, is exactly $\frac{y}{4}$ hours. (This is how long Jóska walked.) Thus:

\[
\frac{x}{6}+\frac{x+y}{60}=\frac{y}{4}
\]

from which $11 x=14 y$.

From the equality, it is clear that $x>y$, meaning Karcsi was wrong when he claimed that the previous stop was closer.

Bohák András (Budapesti Evangélikus Gimn., 9th grade)