2016 AMC 8 第 4 题

先试着解答 2016 AMC 8 第 4 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 2016 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。

4.

奇努小时候能在 33 小时 3030 分钟内跑 1515 英里。现在他年老了,能在 44 小时内走 1010 英里。现在他走一英里比小时候跑一英里多花多少分钟?
When Cheenu was a boy he could run 1515 miles in 33 hours and 3030 minutes. As an old man he can now walk 1010 miles in 44 hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?
66
1010
1515
1818
3030
答案:B
知识点:速率单位换算
小提示:
比较两种速度对应的每英里分钟数
Compare the two paces in minutes per mile.
大提示:
先将 33 小时 3030 分钟转换成分钟,再除以 1515
Convert 33 hours 3030 minutes to minutes before dividing by 1515.
视频讲解:
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文字解答:
为了更容易比较速度,将它们都换成每英里所需分钟数。
小时候他跑 1515 英里用了 3⋅60+30=2103 \cdot 60 + 30 = 210 分钟,所以速度为 21015=14\frac{210}{15} = 14 分钟每英里。
现在他走 1010 英里用了 4⋅60=2404 \cdot 60 = 240 分钟,所以速度为 24010=24\frac{240}{10} = 24 分钟每英里。
相减得,现在他走一英里多花 1010 分钟。
所以正确答案是 B。
To better compare the rates, we can change his speed into minutes per mile.
As a boy he ran 1515 miles in 3⋅60+30=2103 \cdot 60 + 30 = 210 minutes, which means that he ran at a pace of 21015=14\frac{210}{15} = 14 minutes per mile.
As an adult, he can walk 1010 miles in 4⋅60=2404 \cdot 60 = 240 minutes, which means he walks at a pace of 24010=24\frac{240}{10} = 24 minutes per mile.
Subtracting the two, we get that he takes 1010 more minutes to walk a mile as an adult.
Thus, B is the correct answer.
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