2017 AMC 8 第 23 题
先试着解答 2017 AMC 8 第 23 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 2017 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。
23.
连续四天，琳达每天旅行一小时，并且她的速度使她每行进一英里所需分钟数都是整数。第一天之后，每天她的速度都降低，使得每行进一英里所需分钟数比前一天多 分钟。四天中每天她行进的距离也都是整数英里。这四次旅行一共多少英里？
Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?
小提示：
每天每英里所需分钟数必须整除
Each day’s minutes per mile must divide .
大提示：
列出 的因数，并找出四个相差 的因数
List the divisors of and find four of them spaced apart.
视频讲解：
Click to load, then click again to play
文字解答：
琳达每天旅行 分钟。因为每天每英里所需分钟数是整数，且每天行进英里数也是整数，所以每天的每英里分钟数必须是 的因数。 的因数为 、、、、、、、、、、 和 。其中唯一一组四个相邻相差 的数是 、、 和 。四天总路程为 英里。
所以正确答案是 C。
Linda traveled for minutes every day. Since one mile was traveled in an integer amount of minutes each day, her minutes per mile every day must be a factor of The factors of are and The only sequence of four of these numbers that differ by are and For the four days, she traveled miles in total.
Thus, C is the correct answer.
其他年份的第 23 题
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2004 AMC 8
- 2005 AMC 8
- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
- 2009 AMC 8
- 2010 AMC 8
- 2011 AMC 8
- 2012 AMC 8
- 2013 AMC 8
- 2014 AMC 8
- 2015 AMC 8
- 2016 AMC 8
- 2018 AMC 8
- 2019 AMC 8
- 2020 AMC 8
- 2022 AMC 8
- 2023 AMC 8
- 2024 AMC 8
- 2025 AMC 8
- 2026 AMC 8