Question

David 从家开车去机场赶飞机。他第一小时开了 $35$ 英里，但发现如果继续保持这个速度会迟到 $1$ 小时。于是他在剩余路程中把速度提高了 $15$ 英里每小时，结果提前 $30$ 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 $35$ miles in the first hour, but realizes that he will be $1$ hour late if he continues at this speed. He increases his speed by $15$ miles per hour for the rest of the way to the airport and arrives $30$ minutes early. How many miles is the airport from his home?

$140$

$175$

$210$

$245$

$280$

答案：C

知识点：路程、速度与时间方程组

难度评级：1440

解答：

设第一小时后的剩余距离为 $d$ ，距离航班还有 $t$ 小时。若继续以 $35$ 英里每小时行驶，他会迟到一小时，所以 $d=35(t+1)$ 。改以 $50$ 英里每小时行驶，他会提前半小时，所以 $d=50\left(t-\tfrac12\right)$ 。

令两式相等，得到 $35t+35=50t-25$ ，所以 $t=4$ ，且 $d=175$ 。

总路程为 $175+35=210$ 英里。

所以正确答案是 C。

Let $d$ be the remaining distance after one hour and $t$ the remaining time until the flight. At $35$ mph he would be an hour late, so $d=35(t+1).$ At $50$ mph he is half an hour early, so $d=50\left(t-\tfrac12\right).$

Setting these equal gives $35t+35=50t-25,$ so $t=4$ and $d=175.$

The total distance is $175+35=210$ miles.

Thus, the correct answer is C.

2014 AMC 12A 第 11 题

答案：C

难度评级：1440

解答：

其他年份的第 11 题