1992 AMC 8 第 19 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
19.
一条州际公路上第 个出口和第 个出口之间的距离是 英里。如果任意两个出口之间至少相距 英里，那么在第 个和第 个出口之间，相邻两个出口之间最多可以相距多少英里？
The distance between the th and th exits on an interstate highway is miles. If any two exits are at least miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the th and th exits?
答案：C
小提示：
从第 个出口到第 个出口之间有 个间隔。
Between the th and th exits there are gaps
大提示：
要让一个间隔尽可能大，就让其余 个间隔都取允许的最小值 英里。
To make one gap as large as possible, make the other gaps as small as allowed, miles each
解答：
从第 个出口到第 个出口，共有 个相邻出口间隔，每个至少 英里。
要最大化其中一个间隔，就让其他 个间隔都等于 英里，共占 英里。剩下的间隔是 英里。
所以正确答案是 C。
From the th exit to the th exit there are gaps between consecutive exits, each at least miles.
To maximize one gap, make the other gaps exactly miles, using miles. The remaining gap is miles.
Thus, the correct answer is C .
其他年份的第 19 题
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