## 190. Math Puzzle $3 / 81$

The bus line of a city is $20 \mathrm{~km}$ long. Every 15 minutes, a bus departs from each terminal stop, with an average speed of $40 \mathrm{~km} / \mathrm{h}$.

How many buses will you encounter on the way if you travel the entire route? A bus from the opposite direction should just be arriving at the departure time.
For the distance of $20 \mathrm{~km}$, each bus at a speed of $40 \mathrm{~km} / \mathrm{h}$, takes half an hour. This means: Whenever a bus has covered half the distance (after 15 minutes), the next one departs.

When our bus departs, one is just arriving from the opposite direction. A second one is still $\mathrm{mm}$ away from the destination, and a third one is departing from the other terminal stop. We meet the second bus after $5 \mathrm{~km}$, and the third one after $10 \mathrm{~km}$, as we are driving towards each other at the same speed.

By the time we reach the $10 \mathrm{~km}$ mark, another $15 \mathrm{~min}$ have passed. A fourth bus departs from the terminal stop. We meet him after another $5 \mathrm{~km}$.

Upon our arrival at the destination, the fifth bus will just be starting. We meet five buses on our way.