A pedestrian from $A$ at $3 \mathrm{~m} / \mathrm{s}$ and another from $B$ at $6 \mathrm{~m} / \mathrm{s}$ start walking towards the intersection (see the figure). When will they be closest to each other, and what will be the distance between them at that time?

![](https://cdn.mathpix.com/cropped/2024_05_02_198cd9aeaf3bd2c6aa3dg-1.jpg?height=422&width=555&top_left_y=266&top_left_x=774)
After $t$ time has elapsed, the distance between the two pedestrians is: $\sqrt{(30-3 t)^{2}+(40-6 t)^{2}}$. It is sufficient to find the minimum of the square of this expression.

The pedestrians will be closest to each other after $7 \frac{1}{3}$ seconds, at which time their distance will be $\sqrt{80} \mathrm{~m}$.