Question 13
Jenny and Kenny are walking in the same direction, Kenny at $3$ feet per second and Jenny at $1$ foot per second, on parallel paths that are $200$ feet apart. A tall circular building $100$ feet in diameter is centered midway between the paths. At the instant when the building first blocks the line of sight between Jenny and Kenny, they are $200$ feet apart. Let $t$ be the amount of time, in seconds, before Jenny and Kenny can see each other again. If $t$ is written as a fraction in lowest terms, what is the sum of the numerator and denominator?