{"status": "success", "data": {"description_md": "Uryu shoots two arrows which travel arbitrarily close to each other after an indefinite amount of time. For the first second, the first arrow travels $X$ meters, and the distance travelled every second after the first is $Y$ percent of the previous second's distance, for real numbers $0 < X,Y < 100$. The second arrow is shot so that for the first second it travels a distance $Y$, and the distance that arrow travels every second after the first is $X-20$ percent of the distance of the previous second. The sum $X+Y$ is a positive prime $P$. If the minimum solution for $X$ can be represented as $\\frac{a}{b}$ for relatively prime positive integers $a$ and $b$, what is $a+b$?", "description_html": "

Uryu shoots two arrows which travel arbitrarily close to each other after an indefinite amount of time. For the first second, the first arrow travels X meters, and the distance travelled every second after the first is Y percent of the previous second’s distance, for real numbers 0 < X,Y < 100. The second arrow is shot so that for the first second it travels a distance Y, and the distance that arrow travels every second after the first is X-20 percent of the distance of the previous second. The sum X+Y is a positive prime P. If the minimum solution for X can be represented as \\frac{a}{b} for relatively prime positive integers a and b, what is a+b?

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Holiday Contest 2025 - Guts Round - Set 3 Problem 3", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}