3. Little Red Riding Hood is walking along a path at a speed of 6 km/h, while the Gray Wolf is running along a clearing perpendicular to the path at a speed of 8 km/h. When Little Red Riding Hood was crossing the clearing, the Wolf had 80 meters left to run to reach the path. But he was already old, his eyesight was failing, and his sense of smell was not as good. Will the Wolf notice Little Red Riding Hood if he can smell prey only within 45 meters?
3. Answer: No.

Solution. The problem can be solved in a moving coordinate system associated with Little Red Riding Hood. Then Little Red Riding Hood is stationary, and the trajectory of the Wolf's movement is a straight line. The shortest distance from a point to a line here is (by similarity considerations):

$80 \cdot \sin \alpha$, where $\sin \alpha=\frac{3}{5}$. This results in 48 m, which is greater than 45 m.

Another way to solve it: the distance from the intersection point to Little Red Riding Hood, depending on time $t$, is $6 t$; the distance from the intersection point to the Wolf is $80-8 t$. Therefore, the distance from the Wolf to Little Red Riding Hood, by the Pythagorean theorem, is $\sqrt{36 t^{2}+(80-8 t)^{2}}=2 \sqrt{5\left(5 t^{2}-64 t+320\right)}$. The minimum of this value is achieved at $t=\frac{64}{2 \cdot 5}=\frac{32}{5}$, and is equal to 48.