Question

城镇 $A$ 和 $B$ 由一条长 $15$ 英里的直路连接。从 $A$ 到 $B$ 行驶时，每 $5$ 英里限速变化一次：从 $25$ 到 $40$ 再到 $20$ 英里每小时。两辆车分别从 $A$ 和 $B$ 同时出发相向而行，并在每段路上都恰好按限速行驶。两车会在离城镇 $A$ 多少英里处相遇？

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?

$7.75$

$8$

$8.25$

$8.5$

$8.75$

答案：D

知识点：相对速度路程、速度与时间

难度评级：1650

视频讲解：

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文字解答：

把道路看作左、中、右三段。每段长 $5$ 英里。

从 $A$ 出发的车到达中间路段需要小时。 $\frac{5}{25} = \frac{1}{5}$

从 $B$ 出发的车到达中间路段需要小时。到那时，从 $A$ 出发的车已经在中间路段行驶了小时。这辆从 $A$ 出发的车在中间路段已经行驶了英里。 $\frac{5}{20} = \frac{1}{4}$ $\frac{1}{4} - \frac{1}{5} = \frac{1}{20}$ $40 \times \frac{1}{20} = 2$

于是中间路段中两车之间还剩 $5 - 2 = 3$ 英里。

此时从 $A$ 出发的车距离 $A$ 为 $5 + 2 = 7$ 英里。

由于两车在中间路段都以每小时 $40$ 英里的速度行驶，它们再各行 $1.5$ 英里后相遇。因此从 $A$ 出发的车总共行驶 $7 + 1.5 = 8.5$ 英里，选 D。

Think of the road as having three sections: left, middle, and right. Each section is $5$ miles long.

The car from $A$ reaches the middle section in $\frac{5}{25} = \frac{1}{5}$ hours.

The car from $B$ reaches the middle section in $\frac{5}{20} = \frac{1}{4}$ hours. By that time, the car from $A$ has already driven in the middle section for $\frac{1}{4} - \frac{1}{5} = \frac{1}{20}$ hours. During this time, that car from $A$ has traveled $40 \times \frac{1}{20} = 2$ miles in the middle section.

That leaves $5 - 2 = 3$ miles between the two cars in the middle section.

At that moment, the car from $A$ is $5 + 2 = 7$ miles from $A.$

Since the cars drive at the same speed of $40$ mph in the middle section, they meet after each driving $1.5$ more miles. This takes the car from $A$ a total distance of $7 + 1.5 = 8.5$ miles, which is choice D.

2025 AMC 8 第 19 题

答案：D

难度评级：1650

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