2023 AMC 8 第 13 题

先试着解答 2023 AMC 8 第 13 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 2023 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。

13.

在自行车赛路线中,起点和终点之间均匀分布着 77 个补水站,如下图所示。另外还有 22 个维修站也均匀分布在起点和终点之间。第 33 个补水站位于第 11 个维修站之后 22 英里处。这场比赛全长多少英里?
Along the route of a bicycle race, 77 water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also 22 repair stations evenly spaced between the start and finish lines. The 33rd water station is located 22 miles after the 11st repair station. How long is the race in miles?
88
1616
2424
4848
9696
答案:D
知识点:分数比与比例
小提示:
七个补水站把赛程分成 88 个相等间隔
Seven water stations divide the race into 88 equal gaps
大提示:
两个维修站把赛程分成 33 个相等间隔
Two repair stations divide the race into 33 equal gaps
视频讲解:
解答视频缩略图
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文字解答:
第 33 个补水站在全程的 38\frac{3}{8} 处,因为补水站把全程分成 88 个相等间隔。
第一个维修站在全程的 13\frac{1}{3} 处。两站之间的距离占全程的 38−13=124。 \dfrac{3}{8} - \dfrac{1}{3} = \dfrac{1}{24}\text{。}这段距离是 22 英里,所以全程为 24⋅2=4824 \cdot 2 = 48 英里。
所以正确答案是 D。
The 33rd water station is located 38\frac{3}{8} of the way along the race (the water stations split the race up into 88 equal spaces).
The first repair station is located 13\frac{1}{3} of the way along the race. The distance between the stations is 38−13=124 \dfrac{3}{8} - \dfrac{1}{3} = \dfrac{1}{24} of the race length. This distance is 22 miles, so the race is 24⋅2=4824 \cdot 2 = 48 miles long.
Thus, D is the correct answer.
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