Question

Annie 和 Bonnie 正在绕一个 $400$ 米椭圆形跑道跑圈。她们同时出发，但 Annie 已经领先，因为她比 Bonnie 快 $25\%$ 。Annie 第一次追上并超过 Bonnie 时，她已经跑了多少圈？

Annie and Bonnie are running laps around a $400$ -meter oval track. They started together, but Annie has pulled ahead, because she runs $25\%$ faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?

$1\dfrac{1}{4}$

$3\dfrac{1}{3}$

$4$

$5$

$25$

答案：D

知识点：相对速度路程、速度与时间比与比例

难度评级：1240

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文字解答：

因为 Annie 比 Bonnie 快 $25\%$ ，所以 Bonnie 每完成一圈时，Annie 完成 $1 \dfrac{1}{4}$ 圈。也就是说 Bonnie 每跑一圈，Annie 领先四分之一圈。

Annie 要整整领先一圈，需要 Bonnie 完成 $4$ 圈，此时 Annie 完成 $5$ 圈。

所以正确答案是 D。

Since Annie is $25\%$ faster than Bonnie, for every lap Bonnie finishes, Annie completes $1 \dfrac{1}{4}$ laps. Therefore, Annie gains a quarter lap every time Bonnie finishes a lap.

With this in mind, for Annie to completely lap Bonnie, Bonnie must finish $4$ laps, which means that Annie finished $5$ laps.

Thus, D is the correct answer.

2016 AMC 8 第 16 题

答案：D

难度评级：1240

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