Question

一条州际公路上第 $5$ 个出口和第 $26$ 个出口之间的距离是 $118$ 英里。如果任意两个出口之间至少相距 $5$ 英里，那么在第 $5$ 个和第 $26$ 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 $5$ th and $26$ th exits on an interstate highway is $118$ miles. If any two exits are at least $5$ miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the $5$ th and $26$ th exits?

$8$

$13$

$18$

$47$

$98$

答案：C

知识点：极端原理

难度评级：1110

解答：

从第 $5$ 个出口到第 $26$ 个出口，共有 $26 - 5 = 21$ 个相邻出口间隔，每个至少 $5$ 英里。

要最大化其中一个间隔，就让其他 $20$ 个间隔都等于 $5$ 英里，共占 $20 \times 5 = 100$ 英里。剩下的间隔是 $118 - 100 = 18$ 英里。

所以正确答案是 C。

From the $5$ th exit to the $26$ th exit there are $26 - 5 = 21$ gaps between consecutive exits, each at least $5$ miles.

To maximize one gap, make the other $20$ gaps exactly $5$ miles, using $20 \times 5 = 100$ miles. The remaining gap is $118 - 100 = 18$ miles.

Thus, the correct answer is C .

1992 AMC 8 第 19 题

答案：C

难度评级：1110

解答：

其他年份的第 19 题