Firetruck and Area Covered
Source:
January 5, 2007
geometrycalculusAMCAIMEnumber theoryrelatively primeAIME I
Problem Statement
In the middle of a vast prairie, a firetruck is stationed at the intersection of two perpendicular straight highways. The truck travels at miles per hour along the highways and at 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 square miles, where and are relatively prime positive integers. Find