AMC8 2018

AMC8 2018 · Q17

AMC8 2018 · Q17. It mainly tests Fractions, Rates (speed).

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 $2\frac{1}{2}$ feet with each step. How many steps will Bella take by the time she meets Ella?

贝拉从她家开始向朋友艾拉的家步行。与此同时，艾拉开始骑自行车向贝拉家骑行。她们各自保持恒定速度，艾拉骑行的速度是贝拉步行速度的5倍。两家之间的距离是2英里，即10,560英尺，贝拉每步走 $2\frac{1}{2}$ 英尺。到她与艾拉相遇时，贝拉会走多少步？

(A) 704 704

(B) 845 845

(D) 1760 1760

(E) 3520 3520

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): By the time that the two girls meet, Ella will ride $5$ times the distance that Bella walks, so Ella will ride $\frac{5}{6}$ of the total distance, and Bella will walk $\frac{1}{6}$ of the total distance, or $\frac{1}{6}(10,560)=1760$ feet. Each of her steps covers $2\frac{1}{2}=\frac{5}{2}$ feet, so the number of steps she will take is $1760\div\frac{5}{2}=1760\cdot\frac{2}{5}=704$.

答案（A）：当两个女孩相遇时，Ella 骑行的距离是 Bella 步行距离的 $5$ 倍，因此 Ella 骑行总路程的 $\frac{5}{6}$，Bella 步行总路程的 $\frac{1}{6}$，即 $\frac{1}{6}(10,560)=1760$ 英尺。Bella 每一步走 $2\frac{1}{2}=\frac{5}{2}$ 英尺，所以她将走的步数为 $1760\div\frac{5}{2}=1760\cdot\frac{2}{5}=704$。

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