2019 AMC 8 第 5 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

5.

一只乌龟向一只兔子挑战赛跑。兔子欣然同意,很快跑到前面,把行动缓慢的乌龟甩在后面。兔子确信自己会赢,于是停下来打盹。与此同时,乌龟以缓慢而稳定的速度走完整场比赛。兔子醒来后跑向终点,却发现乌龟已经在那里。下列哪幅图符合这场比赛的描述,表示从开始到结束时两者的行进距离 dd 随时间 tt 的变化?

A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance dd traveled by the two animals over time tt from start to finish?

答案:B
知识点:数据与图表解读路程、速度与时间
难度评级:770
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文字解答:

兔子的图像应先快速上升,中间睡觉时保持水平,醒来后再上升。

乌龟则以稳定速度前进,所以是一条直线。

兔子到达终点的时间比乌龟晚,因此兔子图像终点的 xx 值更大。符合这些条件的正是图 BB

正确答案是 B

The hare's path is the one with the horizontal line in the middle, which represents the period when the hare took a nap.

We also know that the time it takes the hare to reach the finish line is longer than the time it took the tortoise.

This means that the end of the hare's path should have a larger xx-value. This is exactly graph B.B.

Thus, the correct answer is B.

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