AMC10 2004 A

AMC10 2004 A · Q17

AMC10 2004 A · Q17. It mainly tests Rates (speed).

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?

Brenda 和 Sally 在一个圆形跑道上朝相反方向跑步，从直径对称的两个点开始。她们第一次相遇时，Brenda 已跑了 100 米。她们第二次相遇时，Sally 已从第一次相遇点多跑了 150 米。每个女孩都以恒定速度跑步。跑道的长度是多少米？

(A) 250 250

(B) 300 300

(D) 400 400

(E) 500 500

Answer

Correct choice: (C)

正确答案：（C）

Solution

When they first meet, they have run a combined distance equal to half the length of the track. Between their first and second meetings, they run a combined distance equal to the full length of the track. Because Brenda runs at a constant speed and runs 100 meters before their first meeting, she runs $2(100) = 200$ meters between their first and second meetings. Therefore the length of the track is $200 + 150 = 350$ meters.

她们第一次相遇时，两人合起来跑的距离等于跑道长度的一半。从第一次到第二次相遇，她们合起来跑的距离等于跑道的完整长度。因为 Brenda 以恒定速度跑步，并在第一次相遇前跑了 100 米，所以从第一次到第二次相遇她跑了 $2(100) = 200$ 米。因此跑道长度为 $200 + 150 = 350$ 米。

Topics

AR.007 Rates (speed)