2004 AMC 8 第 12 题

先试着解答 2004 AMC 8 第 12 题,然后核对你的答案与精心整理的解答,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 2004 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.

妮基通常让手机保持开机。如果手机开着但她实际上没有使用,电池能持续 2424 小时。如果她一直使用,电池只能持续 33 小时。自上次充电以来,她的手机已经开机 99 小时,其中她使用了 6060 分钟。如果她不再通话但保持手机开机,电池还能持续多少小时?
Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for 2424 hours. If she is using it constantly, the battery will last for only 33 hours. Since the last recharge, her phone has been on 99 hours, and during that time she has used it for 6060 minutes. If she doesn’t talk any more but leaves the phone on, how many more hours will the battery last?
77
88
1111
1414
1515
答案:B
知识点:速率分数
小提示:
通话一小时消耗的电量相当于好几个待机小时
One hour of talking uses as much battery as several idle hours.
大提示:
手机待机 88 小时,使用 11 小时
The phone was idle for 88 hours and used for 11 hour.
解答:
不使用时,手机每小时消耗 124\frac{1}{24} 的电量。使用时,每小时消耗 13\frac{1}{3} 的电量。
妮基的手机开机 99 小时,其中 88 小时待机,11 小时通话。
因此手机已消耗 23\frac{2}{3} 的电量。剩余 13\frac{1}{3} 电量在不使用时还能持续 88 小时。
所以正确答案是 B。
When not in use, her cell phone uses up 124\frac{1}{24} of its battery per hour. When it is in use, it uses up 13\frac{1}{3} of its battery per hour.
Niki’s phone has been on for 99 hours, with 88 of those hours being idle and 11 hour being used to talk on the phone.
This means that the phone has used up 23\frac{2}{3} of its battery. In order to drain the remaining 13\frac{1}{3} of the battery, the phone can last for 88 more hours without being used.
Thus, B is the correct answer.
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