2009 AMC 10B Problem 23
Problem 23 of 25HarderAlgebraCounting & Probability
Rachel and Robert run on a circular track. Rachel runs counterclockwise and completes a lap every seconds, and Robert runs clockwise and completes a lap every seconds. Both start from the start line at the same time. At some random time between minutes and minutes after they begin to run, a photographer standing inside the track takes a picture that shows one-fourth of the track, centered on the starting line. What is the probability that both Rachel and Robert are in the picture?
Answer choices
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Solution
The picture spans lap on each side of the start. After seconds Rachel is seconds short of the line; running lap in seconds, she is in view between and seconds of the th minute.
After seconds Robert is seconds from the line; running lap in seconds, he is in view between and seconds.
Both appear between and seconds, a window of length out of so the probability is
Thus, the correct answer is C.