6.3. In the park, all bicycle paths run from north to south or from west to east. Petya and Kolya simultaneously started from point $A$ and rode their bicycles at constant speeds: Petya - along the route $A-B-C$, Kolya - along the route $A-D-E-F-C$ (see fig.), and both spent 12 minutes on the road. It is known that Kolya rides 1.2 times faster than Petya. How much time did he spend on the segment $D E$? The scale in the figure is not preserved.

![](https://cdn.mathpix.com/cropped/2024_05_06_f265a9605ca3fc80eb59g-1.jpg?height=224&width=408&top_left_y=1437&top_left_x=885)
Answer: 1 minute.

Solution. Draw the segment $D H$, as shown in Fig. 2. Kolya travels 1.2 times faster than Petya, so it would take him $12 / 1.2=10$ minutes to travel the route $A-B-C$. The difference in time

![](https://cdn.mathpix.com/cropped/2024_05_06_f265a9605ca3fc80eb59g-2.jpg?height=259&width=279&top_left_y=175&top_left_x=1016)

Fig. 2 $12-10=2$ minutes - this is the time spent moving down the segment $D E$ and moving up the segment $F H$. From the equality $D E=F H$, it follows that Petya will take 1 minute to cover the distance $D E$.

Comment. A correct answer without justification - 2 points.