Question

一名爆破工将引信设定为 $30$ 秒后爆炸。他以每秒 $8$ 码的速度跑开。声音传播速度为每秒 $1080$ 英尺。当爆破工听到爆炸声时，他大约跑了：

A powderman set a fuse for a blast to take place in $30$ seconds. He ran away at a rate of $8$ yards per second. Sound travels at the rate of $1080$ feet per second. When the powderman heard the blast, he had run approximately:

$200$ 码

$200$ yd.

$352$ 码

$352$ yd.

$300$ 码

$300$ yd.

$245$ 码

$245$ yd.

$512$ 码

$512$ yd.

答案：D

知识点：路程、速度与时间单位换算

难度评级：1560

小提示：

设从点燃引信到听见声音的总秒数为 $T$

Let $T$ be the total number of seconds from lighting the fuse until the sound is heard

大提示：

到时刻 $T$ 时，声音已传播 $T-30$ 秒，其路程必须等于爆破工跑出的距离

At time $T$ , the sound has traveled for $T-30$ seconds and must cover the runner’s distance

解答：

设总时间为 $T$ 秒。爆破工与爆炸地点相距 $8T$ 码，即 $24T$ 英尺。因为声音在 $30$ 秒后才开始传播，所以 $1080(T-30)=24T\text{。}$ 因此 $T=\frac{1350}{44}$ 秒，他跑出的距离为 $8T=\frac{2700}{11}\approx245.45\text{ 码}\text{。}$

选项中与之近似的是 $245$ 码，所以正确答案是 D。

Let $T$ be the total time in seconds. The powderman is $8T$ yards, or $24T$ feet, from the blast. Because the sound starts after $30$ seconds, $1080(T-30)=24T.$ Thus $T=\frac{1350}{44}$ seconds, and the distance he ran is $8T=\frac{2700}{11}\approx245.45\text{ yards}.$

Approximately $245$ yards is the listed value, so the correct answer is D.

1952 AMC 12 第 25 题

答案：D

难度评级：1560

小提示：

大提示：

解答：

其他年份的第 25 题