Question

Visvam 每天步行半英里去学校。他的路线由 $10$ 个等长街区组成，每走一个街区需要 $1$ 分钟。今天，在走了 $5$ 个街区后，Visvam 发现他必须绕路，要走 $3$ 个等长街区而不是一个街区才能到达下一个街角。从他开始绕路时起，他必须以多少英里每小时的速度步行，才能按平常时间到达学校？

Visvam walks half a mile to get to school each day. His route consists of $10$ city blocks of equal length and he takes one minute to walk each block. Today, after walking $5$ blocks, Visvam discovers that he has to make a detour, walking $3$ blocks of equal length instead of $1$ block to reach the next corner. From the time he starts his detour, at what speed, in miles per hour, must Visvam walk in order to arrive at school at his usual time?

$4$

$4.2$

$4.5$

$4.8$

$5$

答案：B

知识点：路程、速度与时间单位换算

难度评级：1410

视频讲解：

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文字解答：

半英里对应 $10$ 个街区，所以一个街区长 $\dfrac{1}{2} \div 10 = \dfrac{1}{20}$ 英里。

从绕路开始，Visvam 需要走 $7 \cdot \dfrac{1}{20} = \dfrac{7}{20}$ 英里。

正常情况下，从这个位置到学校需要 $5$ 分钟。现在他需要在这 $5$ 分钟内走完 $\dfrac{7}{20}$ 英里。

注意 $5$ 分钟等于 $\dfrac{5}{60} = \dfrac{1}{12}$ 小时，所以速度为英里每小时。 $\begin{align*} \dfrac{\frac{7}{20}}{\frac{1}{12}} &= 12 \cdot \dfrac{7}{20} \\&= \dfrac{21}{5} \\ &= 4.2 \end{align*}$

正确答案是 B。

If half a mile is the same as $10$ blocks, then one block is $\dfrac{1}{2} \div 10 = \dfrac{1}{20}$ miles.

Starting from the detour, Visvam has to walk $7 \cdot \dfrac{1}{20} = \dfrac{7}{20}$ miles.

Normally, from this spot Visvam would take $5$ minutes to walk to school. Now he has to travel $\dfrac{7}{20}$ miles in $5$ minutes.

Note that $5$ minutes is $\dfrac{5}{60} = \dfrac{1}{12}$ hours. This means his speed must be $\begin{align*} \dfrac{\frac{7}{20}}{\frac{1}{12}} &= 12 \cdot \dfrac{7}{20} \\&= \dfrac{21}{5} \\ &= 4.2 \end{align*}$ mph.

Thus, B is the correct answer.

2023 AMC 8 第 15 题

答案：B

难度评级：1410

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文字解答：

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