2016 AMC 8 第 16 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。
16.
安妮和邦妮正在绕一个 米椭圆形跑道跑圈。她们同时出发，但安妮已经领先，因为她比邦妮快 。安妮第一次追上并超过邦妮时，她已经跑了多少圈？
Annie and Bonnie are running laps around a -meter oval track. They started together, but Annie has pulled ahead, because she runs faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?
小提示：
快 表示同样时间内安妮跑的距离是邦妮的
A faster pace means Annie runs as far as Bonnie in the same time.
大提示：
安妮第一次追上邦妮时，她已经多跑整整一圈
Annie first passes Bonnie when she has gained one full lap.
视频讲解：
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文字解答：
因为安妮比邦妮快 ，所以邦妮每完成一圈时，安妮完成 圈。也就是说，邦妮每跑一圈，安妮领先四分之一圈。
安妮要整整领先一圈，需要邦妮完成 圈，此时安妮完成 圈。
所以正确答案是 D。
Since Annie is faster than Bonnie, for every lap Bonnie finishes, Annie completes 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 laps, which means that Annie finished laps.
Thus, D is the correct answer.
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