Question

Miguel 带着狗 Luna 散步。在公园入口处，他把球直直地向前扔到一棵树旁，然后自己继续以稳定速度向前走。Luna 跑到停在树旁的球那里，再跑回 Miguel 身边。Luna 跑步的速度是 Miguel 走路速度的 $5$ 倍。当 Luna 把球带回 Miguel 身边时，Miguel 已经走过了入口到树之间距离的几分之几？

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?

$\dfrac{1}{6}$

$\dfrac{1}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{2}{5}$

答案：D

知识点：路程、速度与时间比与比例

难度评级：1450

视频讲解：

Click to load, then click again to play

文字解答：

设 Miguel 的速度为 $1$ ，Luna 的速度为 $5$ ，入口到树的距离为 $D$ 。Luna 跑到树需要时间 $D/5$ ，这段时间 Miguel 走了 $D/5$ 。此时两者相距 $4D/5$ ，相向运动的合速度为 $6$ ，所以再过 $2D/15$ 的时间相遇。Miguel 总共走了 $D/5+2D/15=D/3$ ，也就是入口到树距离的 $1/3$ 。

Let the entrance-to-tree distance be $D$ , and let Miguel's speed be $1$ . Luna's speed is $5$ . Luna reaches the tree in time $D/5$ , during which Miguel walks $D/5$ . The remaining distance between Luna and Miguel is $4D/5$ , and they close it at combined speed $6$ , taking time $2D/15$ . Miguel walks a total distance $D/5+2D/15=D/3$ , which is $1/3$ of the entrance-to-tree distance.

2026 AMC 8 第 19 题

答案：D

难度评级：1450

视频讲解：

文字解答：

其他年份的第 19 题