Question

Qiang 以平均每小时 $30$ 英里的速度开了 $15$ 英里。他还需要以每小时 $55$ 英里的速度再开多少英里，才能使整趟旅行的平均速度为每小时 $50$ 英里？

Qiang drives $15$ miles at an average speed of $30$ miles per hour. How many additional miles will he have to drive at $55$ miles per hour to average $50$ miles per hour for the entire trip?

$45$

$62$

$90$

$110$

$135$

答案：D

知识点：路程、速度与时间一次方程

难度评级：1240

视频讲解：

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文字解答：

前 $15$ 英里用时 $\dfrac{15}{30} = \dfrac{1}{2}$ 小时。

设还需开 $x$ 英里，则这段用时为 $\dfrac{x}{55}$ 小时。

整趟路程为 $15 + x$ 英里。平均速度为 $50$ 英里每小时，所以总用时也等于 $\dfrac{x + 15}{50}$ 小时。

令两种总用时相等，得到 $\dfrac{1}{2} + \dfrac{x}{55} = \dfrac{x + 15}{50}.$

交叉相乘并化简得 $15 + x = 25 + \dfrac{10x}{11} \Rightarrow x = 110.$

正确答案是 D。

For the first $15$ miles, Qiang drove for $\dfrac{15}{30} = \dfrac{1}{2}$ an hour.

Let $x$ be the distance that Qiang must drive to satisfy the condition. It will take him $\dfrac{x}{55}$ hours to drive this distance.

The total trip is now $15 + x$ miles. We know the average speed is $50$ miles per hour, so this will take him $\dfrac{x + 15}{50}$ hours.

Setting the two times equal to each other, we get $\dfrac{1}{2} + \dfrac{x}{55} = \dfrac{x + 15}{50}.$

Cross-multiplying and simplifying yields $15 + x = 25 + \dfrac{10x}{11} \Rightarrow x = 110.$

Thus, the correct answer is D.

2019 AMC 8 第 16 题

答案：D

难度评级：1240

视频讲解：

文字解答：

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