AMC 8 2016 Problem 16
AMC8 2016 年第 16 题
行程问题★★★☆☆
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?
Annie 和 Bonnie 绕着 400 米椭圆跑道跑步。他们同时起跑，但是因为 Annie 的速度比 Bonnie 快了 25％，所以她跑到了 Bonnie 的前面。当 Annie 第一次经过 Bonnie 时，Annie 已经跑了多少圈了？
- A.
- B.
- C.4
- D.5
- E.25
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Each lap Bonnie runs, Annie runs another quarter lap, so Bonnie will run four laps before she is overtaken because it takes 4 of of the total lap. to total one lap. When Bonnie runs 4 laps, Annie has gained one full lap and would overtake Bonnie. That means Annie will have run 5 laps.
~ Minor edits by CuteCatKiwi
Saying that Bonnie runs 40 meters per second, then Annie will run 50 meters per second. It will take Bonnie 10 seconds to run 1 lap and it would take 8 seconds for Annie to do 1 lap. The LCM of 8 and 10 is 40. In 40 seconds Bonnie will do 4 laps and Annie will do 5 laps. Since Annie did 1 more lap she passed Bonnie. So the answer is 5 laps.
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