AIME 2026a Problem 1

Faraz started walking at a constant speed along a straight road from his school to the park. One hour after Faraz left, Tanya started running at a constant speed of $2$ miles per hour faster than Faraz walked, following the same straight road from the school to the park. One hour after Tanya left, Jose started bicycling at a constant speed of $7$ miles per hour faster than Tanya ran, following the same straight road from the school to the park. All three people arrived at the park at the same time. The distance from the school to the park is $\frac{m}{n}$ miles, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.