Two towns, $A$ and $B$ , are connected by a straight road, 15 miles long. Traveling from town $A$ to town $B$ , the speed limit changes every 5 miles: from 25 to 40 to 20 miles per hour (mph). Two cars, one at town $A$ and one at town $B$ , start moving toward each other at the same time. They drive at exactly the speed limit in each portion of the road. How far from town $A$ , in miles, will the two cars meet?
A. 7.75
B. 8
C. 8.25
D. 8.5
E. 8.75

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1. 2025 AMC 8 官方解析

Answer (D)：设 $C$ 、 $D$ 分别为距 $A$ 镇 5 英里与 10 英里处。从 $A$ 出发的车到 $C$ 用 $\frac{5}{25}=\frac{1}{5}$ 小时 = 12 分钟；从 $B$ 出发的车到 $D$ 用 $\frac{5}{20}=\frac{1}{4}$ 小时 = 15 分钟。于是 $A$ 车比 $B$ 车早 3 分钟越过各自的分界点，这 3 分钟（ $\frac{1}{20}$ 小时）内 $A$ 车以 40 英里/小时行驶 $40\times\frac{1}{20}=2$ 英里，到达 $E$ 点。此时 $B$ 车恰在 $D$ 点， $E$ 与 $D$ 相距 $5-2=3$ 英里，两车在中段速度相同，故在 $E$ 、 $D$ 正中间相遇，即再走 1.5 英里。所以相遇点距 $A$ 镇 $5+2+1.5=8.5$ 英里。

Answer

D. 8.5

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