AMC8 2026

AMC8 2026 · Q19

AMC8 2026 · Q19. It mainly tests Rates (speed).

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?

米格尔正带着他的狗 Luna 散步。当他们到达公园入口时，米格尔将球直线扔出去，继续以稳定的速度前行。Luna 朝球奔跑，球停在一棵树旁。当狗到达球的地方时，她把球带回给米格尔。Luna 跑的速度是米格尔走路速度的 5 倍。在 Luna 把球带回给米格尔的时候，米格尔走了入口与树之间距离的几分之几？

(A) \frac{1}{6} \frac{1}{6}

(B) \frac{1}{5} \frac{1}{5}

(D) \frac{1}{3} \frac{1}{3}

(E) \frac{2}{5} \frac{2}{5}

Answer

Correct choice: (D)

正确答案：（D）

Solution

Let Miguel's speed equal $s$. That makes Luna's speed $5s$. Let the distance between the park entrance and the tree be $d$. The total distance covered by Miguel and Luna is $s + 5s = 6s$, which is also equal to $2d$. Thus $6s = 2d \Rightarrow s = \boxed{ \textbf{(D) } \frac{1}{3}}$.

设米格尔的速度为 $s$，则 Luna 的速度为 $5s$。设公园入口到树的距离为 $d$。米格尔和 Luna 共同覆盖的总距离为 $s + 5s = 6s$，这也等于 $2d$。因此有 $6s = 2d \Rightarrow s = \boxed{ \textbf{(D) } \frac{1}{3}}$。

Topics

AR.007 Rates (speed)