2013 AMC 8 第 7 题

先试着解答 2013 AMC 8 第 7 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2013 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

7.

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 1010 秒数到 66 节车厢。火车以恒定速度完全通过道口用了 22 分 4545 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 66 cars in the first 1010 seconds. It took the train 22 minutes and 4545 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?
 60\ 60
 80\ 80
 100\ 100
 120\ 120
 140\ 140
答案:C
知识点:比与比例估算
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 1010 秒通过 66 节车厢列出比例式
Use a proportion from 66 cars in 1010 seconds.
视频讲解:
解答视频缩略图
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文字解答:
22 分 4545 秒等于 2⋅60+45=1652 \cdot 60 + 45 = 165 秒。因为 1010 秒通过 66 节车厢,所以设 165165 秒通过 xx 节车厢,满足 610=x165。\dfrac{6}{10}=\dfrac{x}{165}\text{。}
解得 x=165⋅610=99。 x=\dfrac{165\cdot6}{10}=99\text{。} 最接近的选项是 100100。
所以正确答案是 C。
Converting 22 minutes and 4545 seconds into seconds, we get 2⋅60+45=1652 \cdot 60 + 45 = 165 seconds. Since 66 cars passed in 1010 seconds, at the same rate the number of cars xx passing in 165165 seconds satisfies 610=x165.\dfrac{6}{10}=\dfrac{x}{165}.
Solving gives x=165⋅610=99.x=\dfrac{165\cdot6}{10}=99. The closest answer choice is 100100.
Thus, C is the correct answer.
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