2009年AMC10竞赛B第23题
瑞秋和罗伯特在一个圆形跑道上跑步．瑞秋逆时针跑，每隔$90$秒完成一圈，罗伯特顺时针跑，每隔$80$秒完成一圈．两人在同一时间从同一条线上出发．在他们开始跑步后的$10$分钟和$11$分钟之间的某个随机时间，一个站在赛道内的摄影师拍了一张照片，照片显示了以起跑线为中心的四分之一的赛道．瑞秋和罗伯特都在照片上的概率是多少？
课内体系->学科符号->数与式->新定义符号->取最值函数->max{f(x),g(x)} 美国AMC10/12->Knowledge Point->Combination->Probability Calculation->Geometric Models of Probabilities
After $$10$$ minutes ($$600$$ seconds), Rachel will have completed $$6$$ laps and be $$30$$ seconds from completing her seventh lap. Because Rachel runs one-fourth of a lap in $$22.5$$ seconds, she will be in the picture between $$18.75$$ seconds and $$41.25$$ seconds of the tenth minute. After $$10$$ minutes Robert will have completed $$7$$ laps and will be $$40$$ seconds past the starting line. Because Robert runs one-fourth of a lap in $$20$$ seconds, he will be in the picture between $$30$$ and $$50$$ seconds of the tenth minute. Hence both Rachel and Robert will be in the picture if it is taken between $$30$$ and $$41.25$$ seconds of the tenth minute. So the probability that both runners are in the picture is $$\frac{41 .25-30}{60}= \boxed{\frac{3}{16}}$$. The answer is $$\rm(C)$$. 