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2009 AMC 10B Problem 23

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2009 AMC 10B Problem 23AMC 10 Step by Step
Name:                             Date: September 13, 2026
Geometric Probability · difficulty 4 of 5 · about 7 min · position P21-25

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 one-fourth of the track, centered on the starting line. What is the probability that both Rachel and Robert are in the picture?

  1. A)

    116\frac 1{16}

  2. B)

    18\frac 18

  3. C)

    316\frac 3{16}

  4. D)

    14\frac 14

  5. E)

    516\frac 5{16}

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