Two couriers, $A$ and $B$, start from two locations, $M$ and $N$, simultaneously, heading towards $P$. The distance from $N$ to $P$ is $30 \mathrm{~km}$ greater than the distance from $M$ to $P$. Each of them completes their journey in 15 hours. How far is the location $M$ from $P$, if for every $60 \mathrm{~km}$ of the journey, $B$ needs one hour less than $A$?
The distance of location $M$ from $P$ is $x$. $A$ covers the distance in $\frac{15}{x}$ hours, while $B$ does so in $\frac{15}{x+30}$ hours. According to the condition:

$$
60 \frac{15}{x}=60+\frac{15}{x+30}+1
$$

Or

$$
x^{2}+30 x-27000=0
$$

from which the positive root is:

$$
x=150
$$

(Borota Braniszláv, Szeged.)

The problem was solved by: Basch R., Breuer P., Czigler I., Dénes M., Deschán Z., Engler J., Erdős V., Fried E., Gianone O., Grün E., Klein G., Koffler B., Köhler I., Molnár S., Neumann L., Rosenberg E., Setyerov P., Sichermann F., Spitzer L., Szánló L., Szilárd V., Vilcsek A., Viola R., Weinberger Gy.