## 233. Math Puzzle 10/84

Matthias rides a 3 km long street at a constant speed of $v=15 \mathrm{~km} / \mathrm{h}$.

How often and how many city buses overtake him, which run at 5-minute intervals with $v=40 \mathrm{~km} / \mathrm{h}$?
At time $t=0$, when Matthias starts, the first bus should also overtake him. The next one overtakes him after $t_{1}$ hours:

$$
15 t_{1}=40\left(t_{1}-\frac{5}{60}\right)
$$

Matthias' bus with a 5-minute delay $t_{1}=\frac{8}{60} \mathrm{~h}=8 \mathrm{~min}$. During this time, Matthias has traveled $s_{1}=15 \cdot \frac{8}{60}=2$ $\mathrm{km}$

The third bus would overtake him after another 8 minutes, but by then he has already reached his destination. Therefore, only two buses overtake him.