# Problem № 7 (10 points)

A person and his faithful dog started moving along the perimeter of a block from point $A$ simultaneously at time $t_{0}=0$ min. The person moved with a constant speed clockwise, while the dog ran with a constant speed counterclockwise (see figure). It is known that they met for the first time after $t_{1}=2$ min from the start of the movement. This meeting occurred at point $B$. Given that they continued to move in their respective directions and at the same constant speeds, determine the moment of time when they will next be at point $B$ simultaneously. Note that $A B=C D=100$ m, $B C=A D=200$ m.

![](https://cdn.mathpix.com/cropped/2024_05_06_2e80d2c4d366657d3790g-5.jpg?height=422&width=714&top_left_y=1808&top_left_x=702)
# Answer: in 14 min

## Solution and evaluation criteria:

In $t_{1}=2$ min, the person and the dog together covered a distance equal to the perimeter of the block, with the person moving 100 meters from the starting point of the journey.

That is, during each subsequent meeting, the person will be 100 meters away from the location of the previous meeting.

(

The perimeter of the block: $A B+B C+C D+D A=100+200+100+200=600$ meters.

That is, it will take another 12 minutes

And the next time the person and the dog will be at the same point at the moment:

$t_{\kappa}=14$ min.