Question

特雷和妈妈在铁路道口停下来让火车通过。火车刚开始通过时，特雷在前 $10$ 秒数到 $6$ 节车厢。火车以恒定速度完全通过道口用了 $2$ 分 $45$ 秒。下列哪一个最可能是这列火车的车厢数？

Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted $6$ cars in the first $10$ seconds. It took the train $2$ minutes and $45$ seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?

$\ 60$

$\ 80$

$\ 100$

$\ 120$

$\ 140$

答案：C

知识点：比与比例估算

难度评级：900

小提示：

将总通过时间转换为秒

Convert the total crossing time to seconds.

大提示：

利用 $10$ 秒通过 $6$ 节车厢列出比例式

Use a proportion from $6$ cars in $10$ seconds.

视频讲解：

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文字解答：

$2$ 分 $45$ 秒等于 $2 \cdot 60 + 45 = 165$ 秒。因为 $10$ 秒通过 $6$ 节车厢，所以设 $165$ 秒通过 $x$ 节车厢，满足 $\dfrac{6}{10}=\dfrac{x}{165}\text{。}$

解得 $x=\dfrac{165\cdot6}{10}=99\text{。}$ 最接近的选项是 $100$ 。

所以正确答案是 C。

Converting $2$ minutes and $45$ seconds into seconds, we get $2 \cdot 60 + 45 = 165$ seconds. Since $6$ cars passed in $10$ seconds, at the same rate the number of cars $x$ passing in $165$ seconds satisfies $\dfrac{6}{10}=\dfrac{x}{165}.$

Solving gives $x=\dfrac{165\cdot6}{10}=99.$ The closest answer choice is $100$ .

Thus, C is the correct answer.

2013 AMC 8 第 7 题