2018 AMC 8 第 17 题

先试着解答 2018 AMC 8 第 17 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 2018 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。

17.

Bella 从自己家出发,朝朋友 Ella 家走去。与此同时,Ella 从自己家骑自行车朝 Bella 家出发。她们都保持恒定速度,Ella 骑车速度是 Bella 步行速度的 55 倍。两家相距 22 英里,即 10,56010{,}560 英尺,Bella 每一步走 2122 \tfrac{1}{2} 英尺。到两人相遇时,Bella 会走多少步?
Bella begins to walk from her house toward her friend Ella’s house. At the same time, Ella begins to ride her bicycle toward Bella’s house. They each maintain a constant speed, and Ella rides 55 times as fast as Bella walks. The distance between their houses is 22 miles, which is 10,56010{,}560 feet, and Bella covers 2122 \tfrac{1}{2} feet with each step. How many steps will Bella take by the time she meets Ella?
704704
845845
10561056
17601760
35203520
答案:A
知识点:路程、速度与时间比与比例单位换算
小提示:
Ella 的速度是 Bella 的 55 倍,所以把总距离按 1:51:5 分配
Since Ella is 55 times as fast as Bella, split the distance in the ratio 1:51:5.
大提示:
找到 Bella 走的英尺数后,除以每步 2122\frac12 英尺
After finding Bella’s walking distance in feet, divide by 2122\frac12 feet per step.
视频讲解:
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文字解答:
Ella 每骑 55 英尺,Bella 走一英尺,所以相遇时 Bella 走了两家距离的 16\frac16。因此 Bella 走了 16⋅10560=1760\dfrac16 \cdot 10560=1760 英尺。因为她每步走 2.52.5 英尺,到相遇时她走了 17602.5=704\dfrac{1760}{2.5} = 704 步。
所以正确答案是 A。
Since for every foot Bella walks, Ella rides 55 feet, we know that Bella will walk 16\frac16 of the distance between the two houses, and so she walks 16⋅10560=1760\dfrac16 \cdot 10560=1760 feet. Since she walks 2.52.5 feet per step, she takes 17602.5=704\dfrac{1760}{2.5} = 704 steps by the time she meets Ella.
Thus, A is the correct answer.
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