2018 AMC 8 第 12 题

先试着解答 2018 AMC 8 第 12 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。

12.

Sri 车里的钟不准,并且以恒定速度走快。某天他开始购物时,车钟和他准确的手表都显示中午 12:0012{:}00 整。购物结束时,他的手表显示 12:3012{:}30,车钟显示 12:3512{:}35。当天晚些时候,Sri 弄丢了手表。他看车钟,显示 7:007{:}00 整。实际时间是多少?
The clock in Sri’s car, which is not accurate, gains time at a constant rate. One day as he begins shopping he notes that his car clock and his watch (which is accurate) both say 12:0012{:}00 noon. When he is done shopping, his watch says 12:3012{:}30 and his car clock says 12:35.12{:}35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00.7{:}00. What is the actual time?
5:505:50
6:006:00
6:306:30
6:556:55
8:108:10
答案:B
知识点:时钟比与比例
小提示:
比较车钟多走的时间和真实经过的时间
Compare how much time the car clock gains to how much real time passes.
大提示:
车钟的 3535 分钟对应真实的 3030 分钟
The car clock’s 3535 minutes correspond to 3030 actual minutes.
视频讲解:
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文字解答:
从 12:0012:00 中午开始,真实经过 3030 分钟时,车钟走快到经过了 3535 分钟。
因此车钟每走一分钟,真实时间经过 3035=67\frac {30}{35} = \frac 67 分钟。从 12:0012:00 到 7:007:00,车钟走了 7⋅60=4207\cdot 60 = 420 分钟,所以真实时间经过了 420⋅67=360420 \cdot \frac67 = 360 分钟,也就是 66 小时。从 12:0012:00 开始经过 66 小时,实际时间是 6:006:00 。
所以正确答案是 B。
Starting from 12:0012:00 noon, after 3030 minutes of time elapsed, the car clock went 3535 minutes ahead.
Therefore, for every minute the car clock goes ahead, 3035=67 \frac {30}{35} = \frac 67 minutes of actual time pass by. From the time 12:0012:00 to 7:00,7:00, the car clock goes ahead 7⋅60=4207\cdot 60 = 420 minutes, and therefore, 420⋅67=360420 \cdot \frac67 = 360 minutes, or 66 hours, of actual time have passed by. If we start at 12:0012:00 and 66 hours pass by, the time is 6:00.6:00 .
Thus, B is the correct answer.
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