## Task 4 - 320834

A cyclist rode over a $100 \mathrm{~m}$ long bridge at a constant speed. When he had covered $40 \mathrm{~m}$ on this bridge, he met a second cyclist who was coming towards him at the same speed. A car traveling on the same route at a speed of $70 \frac{\mathrm{km}}{\mathrm{h}}$ met the second cyclist at the moment he left the bridge, and it overtook the first cyclist exactly at the end of the bridge.

Determine the speed of the cyclists from these data!
The sought speed of the cyclists is $v$. The time $t_{1}$ during which the first cyclist was on the bridge until he met the second cyclist is exactly as long as the subsequent time $t_{2}$ until the second cyclist left the bridge (and met the car); for in both times $t_{1}$, $t_{2}$ the same distance had to be covered at the same speed $v$.

Therefore, the first cyclist covered an additional $40 \mathrm{~m}$ in the time $t_{2}$ and consequently had to cover $(100-2 \cdot 40) \mathrm{m}=20 \mathrm{~m}$ more in the subsequent time $t_{3}$ to reach the end of the bridge.

In this time $t_{3}$, the car covered the distance of $100 \mathrm{~m}$, which is 5 times the distance covered by the cyclist. Therefore, the speed of the car was 5 times greater than that of the cyclist; i.e., it holds that

$$
v=\frac{70}{5} \frac{\mathrm{km}}{\mathrm{h}}=14 \frac{\mathrm{km}}{\mathrm{h}}
$$

Thus, the sought speed is $14 \frac{\mathrm{km}}{\mathrm{h}}$.