{"status": "success", "data": {"description_md": "A car travels due east at $\\frac 23$ mile per minute on a long, straight road. At the same time, a circular storm, whose radius is 51 miles, moves southeast at $\\frac 12\\sqrt{2}$ mile per minute. At time $t=0,$ the center of the storm is 110 miles due north of the car. At time $t=t_1$ minutes, the car enters the storm circle, and at time $t=t_2$ minutes, the car leaves the storm circle. Find $\\frac 12(t_1+t_2).$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

A car travels due east at \\frac 23 mile per minute on a long, straight road. At the same time, a circular storm, whose radius is 51 miles, moves southeast at \\frac 12\\sqrt{2} mile per minute. At time t=0, the center of the storm is 110 miles due north of the car. At time t=t_1 minutes, the car enters the storm circle, and at time t=t_2 minutes, the car leaves the storm circle. Find \\frac 12(t_1+t_2).

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "1997 AIME Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/97_aime_p08", "prev": "/problem/97_aime_p06"}}