Holiday Contest 2025 - Guts Round - Set 3 Problem 3

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}, what is A+B?