Question

Ashley 开始三小时车程前，汽车里程表读数为 $29792$ ，这是一个回文数，也就是从左到右和从右到左读都相同。到达目的地时，里程表又显示另一个回文数。若 Ashley 从未超过每小时 $75$ 英里的限速，下列哪个是她最大的可能平均速度？

Before Ashley started a three-hour drive, her car's odometer reading was $29792,$ a palindrome. (A palindrome is a number that reads the same way from left to right as it does from right to left.) At her destination, the odometer reading was another palindrome. If Ashley never exceeded the speed limit of $75$ miles per hour, which of the following was her greatest possible average speed?

$33\tfrac13$

$53\tfrac13$

$66\tfrac23$

$70\tfrac13$

$74\tfrac13$

答案：D

知识点：回文数路程、速度与时间极限情形界定

难度评级：1390

解答：

$29792$ 之后的回文数依次为 $29892, 29992, 30003$ ，和 $30103$ 。三小时内最多行驶 $3 \cdot 75 = 225$ 英里。

到 $30103$ 需要行驶 $30103 - 29792 = 311$ 英里，太远。到 $30003$ 需要行驶 $30003 - 29792 = 211$ 英里，平均速度为 $\dfrac{211}{3} = 70\tfrac13$ 英里每小时。

所以正确答案是 D。

The palindromes after $29792$ are $29892, 29992, 30003,$ and $30103.$ In three hours Ashley can drive at most $3 \cdot 75 = 225$ miles.

Reaching $30103$ would require $30103 - 29792 = 311$ miles, which is too far. Reaching $30003$ requires $30003 - 29792 = 211$ miles, giving average speed $\dfrac{211}{3} = 70\tfrac13$ miles per hour.

Thus, the correct answer is D.

1999 AMC 12 第 9 题

答案：D

难度评级：1390

解答：

其他年份的第 9 题