Question

在自行车赛路线中，起点和终点之间均匀分布着 $7$ 个补水站，如下图所示。另外还有 $2$ 个维修站也均匀分布在起点和终点之间。第 $3$ 个补水站位于第 $1$ 个维修站之后 $2$ 英里处。这场比赛全长多少英里？

Along the route of a bicycle race, $7$ water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also $2$ repair stations evenly spaced between the start and finish lines. The $3$ rd water station is located $2$ miles after the $1$ st repair station. How long is the race in miles?

$8$

$16$

$24$

$48$

$96$

答案：D

知识点：分数比与比例

难度评级：1240

视频讲解：

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文字解答：

第 $3$ 个补水站在全程的 $\frac{3}{8}$ 处，因为补水站把全程分成 $8$ 个相等间隔。

第一个维修站在全程的 $\frac{1}{3}$ 处。两者相差个全程。这段距离是 $2$ 英里，所以全程为 $24 \cdot 2 = 48$ 英里。 $\dfrac{3}{8} - \dfrac{1}{3} = \dfrac{1}{24}$

正确答案是 D。

The $3$ rd water station is located $\frac{3}{8}$ of the way along the race (the water stations split the race up into $8$ equal spaces).

The first repair station is located $\frac{1}{3}$ of the way along the race. The distance between the two is $\dfrac{3}{8} - \dfrac{1}{3} = \dfrac{1}{24}$ the length of the race. We know that this equals $2,$ which means the race is $24 \cdot 2 = 48$ miles long.

Thus, D is the correct answer.

2023 AMC 8 第 13 题

答案：D

难度评级：1240

视频讲解：

文字解答：

其他年份的第 13 题