2026 AMC 8 Problem 19

Miguel is walking with his dog, Luna. When they reach the entrance to a park, Miguel throws a ball straight ahead and continues to walk at a steady pace. Luna sprints toward the ball, which stops by a tree. As soon as the dog reaches the ball, she brings it back to Miguel. Luna runs 5 times faster than Miguel walks. What fraction of the distance between the entrance and the tree does Miguel cover by the time Luna brings him the ball?

\textbf{(A)} \dfrac{1}{6} \qquad \textbf{(B)} \dfrac{1}{5} \qquad \textbf{(C)} \dfrac{1}{4} \qquad \textbf{(D)} \dfrac{1}{3} \qquad \textbf{(E)} \dfrac{2}{5}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.