2014 AMC 12A 第 11 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。
11.
David 从家开车去机场赶飞机。他第一小时开了 英里，但发现如果继续保持这个速度会迟到 小时。于是他在剩余路程中把速度提高了 英里每小时，结果提前 分钟到达。机场离他家多少英里？
David drives from his home to the airport to catch a flight. He drives miles in the first hour, but realizes that he will be hour late if he continues at this speed. He increases his speed by miles per hour for the rest of the way to the airport and arrives minutes early. How many miles is the airport from his home?
小提示：
设第一小时后离航班还有 小时，并把剩余距离用两种方式表示。
Let be the time still needed after the first hour, and write the remaining distance two ways
大提示：
剩余距离 满足 和 。
The leftover distance satisfies and
解答：
设第一小时后的剩余距离为 ，距离航班还有 小时。若继续以 英里每小时行驶，他会迟到一小时，所以 。改以 英里每小时行驶，他会提前半小时，所以 。
令两式相等，得到 ，所以 ，且 。
总路程为 英里。
所以正确答案是 C。
Let be the remaining distance after one hour and the remaining time until the flight. At mph he would be an hour late, so At mph he is half an hour early, so
Setting these equal gives so and
The total distance is miles.
Thus, the correct answer is C.
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