AMC 8 2022 Problem 10
AMC8 2022 年第 10 题
行程问题★★☆☆☆
One sunny day, Ling decided to take a hike in the mountains. She left her house at 8 AM , drove at a constant speed of 45 miles per hour, and arrived at the hiking trail at 10 AM . After hiking for 3 hours, Ling drove home at a constant speed of 60 miles per hour. Which of the following graphs best illustrates the distance between Ling's car and her house over the course of her trip?
在一个晴朗的日子，Ling 决定去山里远足。她早上 8 时离开家，以每小时 45 英里的恒定速度开车，在早上 10 时到达登山径。徒步运动 3 小时后，Ling 以每小时 60 英里的恒定速度开车回家。以下哪张图最好的表达了 Ling 的行程中她的汽车和她家之间的距离？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
It took Ling 2 2 hours to drive from her house to the hiking trail, driving at a speed of 45 45 miles per hour. This means the trail was 2 ⋅ 45 = 90 2⋅45=90 miles from her house. She arrived at 10 𝐴 𝑀 10 AM and hiked for 3 3 hours, so she left the trail at 1 𝑃 𝑀 1 PM. She then drove home, covering a distance of 90 90 miles at a speed of 60 60 miles per hour. Hence the return trip took 90 ÷ 60 = 1.5 90÷60=1.5 hours, and Ling arrived at home at 2: 30 2:30 PM. Graphs ( 𝐴 ) (A) and ( 𝐸 ) (E) are the only ones where Ling drove 90 90 miles to reach the trail. Graphs ( 𝐶 ) (C) and ( 𝐸 ) (E) are the only ones where she returns home at 2: 30 𝑃 𝑀 2:30PM. This means the correct answer must be ( 𝐸 ) (E). Answer: 𝐸 E .
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