1997 AIME Problem 7

A car travels due east at \frac 23 miles 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} miles 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.