Question

Brenda 和 Sally 在一条圆形跑道上沿相反方向跑步，从直径两端的点同时出发。她们第一次相遇时，Brenda 已跑了 $100$ 米。她们下一次相遇时，Sally 已经从第一次相遇点又跑了 $150$ 米。两人的速度都恒定。跑道长多少米？

Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run $100$ meters. They next meet after Sally has run $150$ meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

$250$

$300$

$350$

$400$

$500$

答案：C

知识点：相对速度路程、速度与时间比与比例

难度评级：1540

小提示：

到第一次相遇时，两人合计跑了半圈。

By the first meeting the two together have covered half the track

大提示：

第一次和第二次相遇之间，两人合计跑了一整圈，所以 Brenda 跑了第一次路程的两倍。

Between the first and second meetings they together cover a full track, so Brenda runs twice her first leg

解答：

从相对两端出发时，她们第一次相遇时合计跑了半个跑道长度。

第一次和第二次相遇之间，她们合计跑了一个完整跑道长度。因为 Brenda 第一次相遇前跑了 $100$ 米，所以这段时间她跑了 $2 \cdot 100 = 200$ 米。

同一时间段内 Sally 跑了 $150$ 米，因此跑道长度为 $200 + 150 = 350$ 米。

所以正确答案是 C。

Starting at opposite ends, when they first meet they have together run half the track. Between the first and second meetings, they together run a full track length.

Since Brenda runs at a constant speed and covered $100$ meters before the first meeting, she covers $2 \cdot 100 = 200$ meters between the two meetings.

Adding Sally’s $150$ meters over that same interval gives a track length of $200 + 150 = 350$ meters.

Thus, the correct answer is C.

2004 AMC 12A 第 15 题

答案：C

难度评级：1540

小提示：

大提示：

解答：

其他年份的第 15 题