# Problem № 7 (10 points)

A person and his faithful dog started moving along the perimeter of a block from point A at the same time $t_{0}=0$ min. The person moved with a constant speed clockwise, while the dog ran with a constant speed counterclockwise (see fig.). It is known that they met for the first time after $t_{1}=1$ min from the start of the movement. This meeting occurred at point $B$. Given that they continued to move in the same direction and at the same speed after this, determine at what moment in time they will next be at point $B$ simultaneously. Note that $A B=C D=100$ m, $B C=A D=300$ m.

![](https://cdn.mathpix.com/cropped/2024_05_06_2e80d2c4d366657d3790g-2.jpg?height=422&width=714&top_left_y=1805&top_left_x=702)
# Answer: in 9 min

## Solution and evaluation criteria:

In $t_{1}=1$ 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.

Perimeter of the block: $A B+B C+C D+D A=100+300+100+300=800$ meters.

So, it will take another 8 minutes.

And the next time the person and the dog will be at the point at the moment: $t_{\kappa}=9$ min.