Question

Chantal 和 Jean 从登山口出发，沿小路走向一座消防塔。Jean 背着很重的背包，走得较慢。Chantal 开始时以每小时 $4$ 英里的速度行走。到消防塔的一半路程处，小路变得很陡，她放慢到每小时 $2$ 英里。到达消防塔后，她立即掉头，并以每小时 $3$ 英里的速度下行陡峭的那一段。她在半程点遇到 Jean。到他们相遇为止，Jean 的平均速度是多少英里每小时？

Chantal and Jean start hiking from a trailhead toward a fire tower. Jean is wearing a heavy backpack and walks slower. Chantal starts walking at $4$ miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to $2$ miles per hour. After reaching the tower, she immediately turns around and descends the steep part of the trail at $3$ miles per hour. She meets Jean at the halfway point. What was Jean's average speed, in miles per hour, until they meet?

$\dfrac{12}{13}$

$1$

$\dfrac{13}{12}$

$\dfrac{24}{13}$

$2$

答案：A

知识点：路程、速度与时间

难度评级：1140

视频讲解：

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文字解答：

设到消防塔的全程距离为 $2d$ ，其中 $d > 0$ 。

Chantal 一共用时小时。 $\dfrac{d}{4} + \dfrac{d}{2} + \dfrac{d}{3} = \dfrac{13d}{12}$

Jean 在 $\dfrac{13d}{12}$ 小时内走了 $d$ 英里，所以他的平均速度为 $d \div \dfrac{13d}{12} = \dfrac{12}{13}$

所以正确答案是 A。

Let $2d$ be the distance from the trailhead to the fire tower, where $d > 0.$

Then Chantal hiked for $\dfrac{d}{4} + \dfrac{d}{2} + \dfrac{d}{3} = \dfrac{13d}{12}$ hours.

If Jean travelled $d$ miles in $\dfrac{13d}{12}$ hours, then his speed was $d \div \dfrac{13d}{12} = \dfrac{12}{13}$ miles per hour.

Thus, A is the correct answer.

2021 AMC 10A Spring 第 6 题

答案：A

难度评级：1140

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文字解答：

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