2026 AMC 8 第 19 题
先试着解答 2026 AMC 8 第 19 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2026 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
19.
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 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 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?
小提示：
设入口到树的距离为 。
Let the entrance-to-tree distance be
大提示：
Luna 到达树后，Luna 和 Miguel 相向运动。
After Luna reaches the tree, Miguel and Luna move toward each other
视频讲解：
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文字解答：
设 Miguel 的速度为 ，Luna 的速度为 ，入口到树的距离为 。Luna 跑到树需要时间 ，这段时间 Miguel 走了 。此时两者相距 ，相向运动的合速度为 ，所以再过 的时间相遇。Miguel 总共走了 ，也就是入口到树距离的 。
Let the entrance-to-tree distance be , and let Miguel’s speed be . Luna’s speed is . Luna reaches the tree in time , during which Miguel walks . The remaining distance between Luna and Miguel is , and they close it at combined speed , taking time . Miguel walks a total distance , which is of the entrance-to-tree distance.
其他年份的第 19 题
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