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 \(\frac 12(t_1+t_2)\).
(第十五届AIME1997 第7题)