{"status": "success", "data": {"description_md": "Alain and Louise are driving on a circular track with radius 25 km. Alain leaves the starting line first, going clockwise around the track at a speed of 80 km/h. Fifteen minutes after Alain starts, Louise leaves the same starting line, going counter-clockwise around the track at a speed of 100 km/h. For how many hours will Louise have been driving when the two of them pass each other for the fourth time?\n\n$\\text{(A)}\\ \\frac{50\\pi-6}{45}\\qquad\\text{(B)}\\ \\frac{4\\pi+1}{4}\\qquad\\text{(C)}\\ \\frac{10\\pi-1}{9}\\qquad\\text{(D)}\\ \\frac{15\\pi+6}{16}\\qquad\\text{(E)}\\ \\frac{25\\pi-1}{24}$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "

Alain and Louise are driving on a circular track with radius 25 km. Alain leaves the starting line first, going clockwise around the track at a speed of 80 km/h. Fifteen minutes after Alain starts, Louise leaves the same starting line, going counter-clockwise around the track at a speed of 100 km/h. For how many hours will Louise have been driving when the two of them pass each other for the fourth time?

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\\text{(A)}\\ \\frac{50\\pi-6}{45}\\qquad\\text{(B)}\\ \\frac{4\\pi+1}{4}\\qquad\\text{(C)}\\ \\frac{10\\pi-1}{9}\\qquad\\text{(D)}\\ \\frac{15\\pi+6}{16}\\qquad\\text{(E)}\\ \\frac{25\\pi-1}{24}

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Cayley, by CEMC, is licensed under the CC BY-NC 3.0 DEED. They are not affiliated with or endorse TopsOJ in any way.

\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2016 Cayley Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/16_cayley_p23", "prev": "/problem/16_cayley_p21"}}