## 24. Math Puzzle $5 / 67$

A pedestrian walking along a tram line noticed that a tram overtook him every 12 minutes and that a tram of this line approached him every 4 minutes. The pedestrian walked at a constant speed, as did the tram on this section of the route.

At what time interval do the trams operate on this tram line?
The distance between the trams is $x$. Since the pedestrian is walking in the direction of travel and is overtaken by a tram every 12 minutes, this means that the tram covers this distance in 12-x minutes. For the distance that the pedestrian takes 1 minute to cover, the tram needs $\frac{12-x}{12}$ minutes. In the opposite direction, the tram only needs $\frac{x-4}{4}$ minutes. This results in the equation

$$
\frac{12-x}{12}=\frac{x-4}{4} \rightarrow x=6 \text { minutes }
$$