{"status": "success", "data": {"description_md": "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?\n\n$\\text{(A) } \\frac 1{16}\n\\qquad\n\\text{(B) } \\frac 18\n\\qquad\n\\text{(C) } \\frac 3{16}\n\\qquad\n\\text{(D) } \\frac 14\n\\qquad\n\\text{(E) } \\frac 5{16}$", "description_html": "<p>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?</p>\n<p> <span class=\"katex--inline\">\\text{(A) } \\frac 1{16}\n\\qquad\n\\text{(B) } \\frac 18\n\\qquad\n\\text{(C) } \\frac 3{16}\n\\qquad\n\\text{(D) } \\frac 14\n\\qquad\n\\text{(E) } \\frac 5{16}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2009 AMC 10B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10B_p24", "prev": "/problem/09_amc10B_p22"}}