A courier departs from $A$ towards $B$; at the same time, another courier departs from $B$ towards $A$. They meet after 8 hours. How many $\mathrm{km}$ does each courier travel per hour, if the distance from $A$ to $B$ is $176 \mathrm{~km}$ and it takes one courier 1 hour longer to travel $60 \mathrm{~km}$ than it takes the other courier?
If one courier does it in $x$ hours, then the other does it in $x+1$ hours, covering $60 \mathrm{~km}$. Therefore, they cover $\frac{60}{x}$ and $\frac{60}{x+1}$ km per hour, respectively, so

$$
8 \cdot \frac{60}{x} + 8 \cdot \frac{60}{x+1} = 176
$$

or, rearranged,

$$
11 x^{2} - 49 x - 60 = 0
$$

Since the positive root of this equation is $x=5$, one courier covers $12 \mathrm{~km}$ and the other $10 \mathrm{~km}$ per hour.

(Gábor Czukor, Budapest.)

The problem was also solved by: L. Bánó, J. Baumgarten, K. Bendl, B. Csernyi, E. Dévai, J. Dévai, F. Eckhart, V. Eckstein, P. Ehrenstein, S. Erdélyi, M. Fekete, E. Freund, A. Fuchs, P. Füstös, D. Goldstein, E. Tandlich, Z. Harsányi, E. Havas, P. Heimlich, Gy. Jánosy, F. Kemény, J. Kepes, J. Kiss, Gy. Klein, B. Koffer, B. Lázár, J. Mangold, K. Miklóssy, I. Nagel, A. Paunz, S. Pichler, E. Rajz, E. Reiner, E. Sárközy, Gy. Schlesinger, Gy. Schuster, J. Steiger, B. Tóth, M. Vámos, V. Wáhl, Renée Wottitz.