{"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 start 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$\\textbf{(A)}\\ \\frac {1}{16}\\qquad \\textbf{(B)}\\ \\frac18\\qquad \\textbf{(C)}\\ \\frac {3}{16} \\qquad \\textbf{(D)}\\ \\frac14\\qquad \\textbf{(E)}\\ \\frac {5}{16}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Rachel and Robert run on a circular track. Rachel runs counterclockwise and completes a lap every  <span class=\"katex--inline\">90</span>  seconds, and Robert runs clockwise and completes a lap every  <span class=\"katex--inline\">80</span>  seconds. Both start from the start line at the same time. At some random time between  <span class=\"katex--inline\">10</span>  minutes and  <span class=\"katex--inline\">11</span>  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>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac {1}{16}\\qquad \\textbf{(B)}\\ \\frac18\\qquad \\textbf{(C)}\\ \\frac {3}{16} \\qquad \\textbf{(D)}\\ \\frac14\\qquad \\textbf{(E)}\\ \\frac {5}{16}</span> </p>&#10;<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": 3, "problem_name": "2009 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12B_p19", "prev": "/problem/09_amc12B_p17"}}