270. The Runner's Puzzle. $A B C D$ is a square field with an area of 19.36 hectares. $B E$ is a straight path, and $E$ is 110 meters from $D$. During the competition, Adams ran straight from $A$ to $D$, while Brown started running from $B$, reached $E$, and then continued towards $D$.

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-080.jpg?height=591&width=529&top_left_y=321&top_left_x=772)

Each ran at a constant speed, and when Brown reached $E$, he saw Adams 30 meters ahead of him.

Who won the competition and by what margin?
270. Each side of the field is 440 m, \(B A E\) is a right-angled triangle. Therefore, \(A E=330\) m, \(B E=550\) m. If Brown runs 550 m in the same time it takes Adams to run 360 m \((330+30)\), then Brown can run the remaining 100 m in the time it takes Adams to run only \(72 \mathrm{m}\). But \(30+72=102 \mathrm{m}\), so Brown wins, beating his opponent by 8 m.

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-238.jpg?height=505&width=468&top_left_y=570&top_left_x=797)