In the middle of a vast prairie, a firetruck is stationed at the intersection of two perpendicular straight highways. The truck travels at $$50$$ miles per hour along the highways and at $$14$$ miles per hour across the prairie. Consider the set of points that can be reached by the firetruck within six minutes. The area of this region is $$\frac{m}{n}$$ square miles, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m + n$$.

(第十八届AIME1 2000 第13题)