AMC 8 2018 Problem 17
AMC8 2018 年第 17 题
行程问题★★★☆☆
Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides 5 times as fast as Bella walks. The distance between their houses is 2 miles, which is 10,560 feet, and Bella covers feet with each step. How many steps will Bella take by the time she meets Ella?
Bella 开始从她家步行去她朋友 Ella 的家。同时，Ella 骑着自行车开始向 Bella 的家出发。她们均保持各自恒定的速度，并且 Ella 骑车的速度是 Bella 行走速度的 5 倍。她们家相距 2 英里，即 10,560 英尺，已知 Bella 每步长为 英尺，那么当 Bella 和 Ella 相遇时，Bella 走了多少步？
- A.704
- B.845
- C.1056
- D.1760
- E.3520
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
By the time that the two girls meet, Ella will ride 5 5 times the distance that Bella walks, so Ella will ride 5 6 6 5 of the total= distance, and Bella will walk 1 6 6 1 of the total distance, or 1 6 ( 10, 560 ) = 1760 6 1 (10,560)=1760 feet. Each of her steps covers 2 1 2 2 2 1 = 5 2 2 5 feet, so the number of steps she will take is 1760 ÷ 5 2 1760÷ 2 5 = 1760 ⋅ 2 5 = 704 1760⋅ 5 2 =704. 𝑂 𝑅 OR Bella's rate is 2.5 2.5 feet per step whereas Ella travels 12.5 12.5 feet for each of Bella's steps. So together they travel 15 feet for each of Bella's steps. Hence the number of steps taken by Bella when she meets Ella is 10, 560 15 = 704 15 10,560 =704. Answer: 𝐴 A .
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