Question

David 从家开车去机场赶飞机。第一小时他开了 $35$ 英里，但意识到如果继续按这个速度行驶会迟到 $1$ 小时。之后他把速度提高 $15$ 英里每小时，并提前 $30$ 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、速度与时间一次方程

难度评级：1540

解答：

第一小时后，David 的速度为 $50$ 英里每小时。

若机场离家 $x$ 英里，则两种行程时间相差一个半小时，因此解方程：所以机场离家 $x=210$ 英里。 $\dfrac x{35} - \left(1+\dfrac{x-35}{50}\right) = \dfrac 32$ $\begin{aligned} \dfrac x{35} - \left(1+\dfrac{x-35}{50}\right) &= \dfrac 32\\ \dfrac x{35} - \dfrac{x-35+50}{50} &= \dfrac 32\\ 10x - 7(x+15)&= 525\\ 10x - 7x-105&= 525\\ 3x&= 630\\ x&=210 \end{aligned}$

所以正确答案是 C。

Note that David drives at $50$ miles per hour after one hour.

Then, if the airport is $x$ miles from David's house, we know that: $\dfrac x{35} - \left(1+\dfrac{x-35}{50}\right) = \dfrac 32$ We solve this equation as follows: $\begin{aligned} \dfrac x{35} - \left(1+\dfrac{x-35}{50}\right) &= \dfrac 32\\ \dfrac x{35} - \dfrac{x-35+50}{50} &= \dfrac 32\\ 10x - 7(x+15)&= 525\\ 10x - 7x-105&= 525\\ 3x&= 630\\ x&=210 \end{aligned}$ Therefore, the airport is $x=210$ miles from David's house.

Thus, C is the correct answer.

2014 AMC 10A 第 15 题

答案：C

难度评级：1540

解答：

其他年份的第 15 题