Question

某东西向公路上，两个方向的车流均以每小时 $60$ 英里的恒定速度行驶。一名向东行驶的司机在五分钟内经过 $20$ 辆向西行驶的车。假设向西车道中的车辆等距排列。下列哪个数最接近一段 $100$ 英里公路上向西行驶车辆的数量？

The traffic on a certain east-west highway moves at a constant speed of $60$ miles per hour in both directions. An eastbound driver passes $20$ westbound vehicles in a five-minute interval. Assume vehicles in the westbound lane are equally spaced. Which of the following is closest to the number of westbound vehicles present in a $100$ -mile section of highway?

$100$

$120$

$200$

$240$

$400$

答案：C

知识点：相对速度路程、速度与时间比与比例

难度评级：1360

小提示：

两车接近的相对速度等于它们速度之和

The cars approach one another at the sum of their speeds

大提示：

用相对速度下行驶的距离求向西车辆的间距

Use the distance covered at relative speed to find the spacing between westbound vehicles

解答：

相对速度为每小时 $120$ 英里，所以五分钟内司机相对行驶 $10$ 英里。在这段距离内经过 $20$ 辆等距车辆，间距约为 $\frac{10}{20}=\frac{1}{2}$ 英里。因此一段 $100$ 英里的公路约有 $\frac{100}{\frac{1}{2}}=200$ 辆车。

所以正确答案是 C。

The relative speed is $120$ miles per hour, so in five minutes the driver covers $10$ relative miles. Passing $20$ equally spaced vehicles in that distance means the spacing is about $\frac{10}{20}=\frac{1}{2}$ mile. Thus a $100$ -mile section contains about $\frac{100}{\frac{1}{2}}=200$ vehicles.

Thus the correct answer is C.

1989 AMC 12 第 12 题

答案：C

难度评级：1360

小提示：

大提示：

解答：

其他年份的第 12 题