1522. 
Rachel and Robert run on a circular track. Rachel runs counterclockwise and completes a lap every 90 seconds, and Robert runs clockwise and completes a lap every 80 seconds. Both start from the same line at the same time. At some random time between 10 minutes and 11 minutes after they begin to run, a photographer standing inside the track takes a picture that shows onefourth of the track, centered on the starting line. What is the probability that both Rachel and Robert are in the picture?
This problem is copyrighted by the American Mathematics Competitions.

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