A scout robot is trapped at the center of a square with side length 1km. The scout robot can move at a speed of 3km/h. A guard robot is located at a vertex of the square, and patrols the boundary of the square at a speed of 9km/h. The guard robot is powered by an electric wire, restricting its movement to the boundary line of the square. Both robots can always see each other and make real-time decisions based on the available information.
Explain how the scout robot can escape the square without encountering the guard robot. Also, suggest a speed of the scout robot, as low as you can, on which it can escape the square.
I tried two main methods. First, I attempted to create a parametric equation by drawing a straight line at each moment. Second, I attempted to calculate and narrow down the range from which I could escape in each situation.
However, because it is a real-time problem, the formula is very complicated and I need help figuring out how to calculate it. (Except the problem is that I used a translator so it may have been misrepresented)
