2004年AMC10竞赛A第17题 2004年AMC12竞赛A第15题
$$2004-AMC10A-18$$  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 在圆形轨道上以相反的方向奔跑，分别从一条直径的两个端点开始。 他们在 Brenda 跑了 100 米后第一次见面。 在 Sally 跑过他们的第一个会面点 150 米后，他们下一次见面。 每个女孩都以恒定的速度奔跑。 轨道的长度是多少米？
美国AMC10/12->Knowledge Point->Algebra->Application->Equation Word Problems 课内体系->知识点->等式与不等式->等式->方程组的解集
Call the length of the race track $$x$$. When they meet at the first meeting point, Brenda has run $$100$$ meters, while Sally has run $$\dfrac{x}{2}-100$$ meters. By the second meeting point, Sally has run $$150$$ meters, while Brenda has run $$x-150$$ meters. Since they run at a constant speed, we can set up a proportion: $$\dfrac{100}{x-150}=\dfrac{\dfrac{x}{2}-100}{150}$$. Cross-multiplying, we get that $$x=350\Rightarrow\boxed {(\text{C})350}$$.  Sidenote by carlos $$8$$:  Since they run at constant speeds, Brenda must\textquotesingle ve ran $$200$$ meters to get to the second meeting point, therefore we can make an equation $$200=x-150$$, solving for $$x$$, gives us our answer $$350$$.  The total distance the girls run between the start and the first meeting is one half of the track length. The total distance they run between the two meetings is the track length. As the girls run at constant speeds, the interval between the meetings is twice as long as the interval between the start and the first meeting. Thus between the meetings Brenda will run $$2\times100=200$$ meters. Therefore the length of the track is $$150+200=350$$ meters $$\Rightarrow \boxed {(\text{C})350}$$. 