2002年AMC10竞赛B第21题 2002年AMC12竞赛B第17题
$$2002-AMC12B-17$$  Andy's lawn has twice as much area as Beth's lawn and three times as much area as Carlos' lawn. Carlos' lawn mower cuts half as fast as Beth's mower and one third as fast as Andy's mower. If they all start to mow their lawns at the same time, who will finish first?  安迪的草坪面积是贝丝草坪的两倍，是卡洛斯草坪的三倍。 卡洛斯的割草机的割草速度是贝丝的割草机的一半，是安迪的割草机的三分之一。 如果他们同时开始修剪草坪，谁会先完成？
美国AMC10/12->Knowledge Point->Algebra->Application->Proportion Word Problems 课内体系->知识点->函数的应用->函数的实际应用->分式函数模型
We say Andy\textquotesingle s lawn has an area of $$x$$. Beth\textquotesingle s lawn thus has an area of $$\dfrac{x}{2}$$, and Carlos\textquotesingle s lawn has an area of $$\dfrac{x}{3}$$.  We say Andy\textquotesingle s lawn mower cuts at a speed of $$y$$. Carlos\textquotesingle s cuts at a speed of $$\dfrac{y}{3}$$, and Beth\textquotesingle s cuts at a speed $$\dfrac{2y}{3}$$.  Each person\textquotesingle s lawn is cut at a speed of $$\dfrac{\rm area}{\rm rate}$$, so Andy\textquotesingle s is cut in $$\dfrac{x}{y}$$ time, as is Carlos\textquotesingle s. Beth\textquotesingle s is cut in $$\dfrac{3}{4}\times\dfrac{x}{y}$$, so the first one to finish is Beth. 