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)