AMC8 2016

AMC8 2016 · Q16

AMC8 2016 · Q16. It mainly tests Rates (speed), Arithmetic misc.

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 在一个 400 米椭圆跑道上跑圈。她们一起起跑，但 Annie 已经领先，因为她的速度比 Bonnie 快 25%。当她第一次超过 Bonnie 时，Annie 会跑完多少圈？

(A) $1/4$ $1/4$

(B) $1/3$ $1/3$

(D) 5 5

(E) 25 25

Answer

Correct choice: (D)

正确答案：（D）

Solution

Let N be the number of laps run by Annie when she passes Bonnie for the first time. The number of laps run by Bonnie is N-1. Then $\frac{N}{N-1}=1.25=\frac{5}{4}$. So $N=5$.

设 $N$ 为安妮第一次追上邦妮时安妮跑过的圈数。此时邦妮跑过的圈数为 $N-1$。于是有 $\frac{N}{N-1}=1.25=\frac{5}{4}$，所以 $N=5$。

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