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 6 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 ?
A. $\frac{1}{6}$
B. $\frac{1}{5}$
C. $\frac{2}{7}$
D. $\frac{1}{3}$
E. $\frac{2}{5}$

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Worked solution

1. 2026 AMC 8 官方解析

图示：
$A$ （公园入口）， $C$ （相遇点）， $B$ （树）
$M$ 走过 $AC = 1$ 份；
$L$ 走过 $AB + BC = 1 + 2.5 + 2.5 = 6$ 份。

$S_M : S_L = 1 : 6 \quad AC : AB = 1 : 3.5 = 2 : 7$ ,
$M$ 走过路程占全程的 $\frac{2}{7}$ .

Answer

C. $\frac{2}{7}$

AI analysis — may contain mistakes.

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