2012 AIME II Problems/Problem 4

Problem 4

Ana, Bob, and Cao bike at constant rates of meters per second, meters per second, and meters per second, respectively. They all begin biking at the same time from the northeast corner of a rectangular field whose longer side runs due west. Ana starts biking along the edge of the field, initially heading west, Bob starts biking along the edge of the field, initially heading south, and Cao bikes in a straight line across the field to a point on the south edge of the field. Cao arrives at point at the same time that Ana and Bob arrive at for the first time. The ratio of the field's length to the field's width to the distance from point to the southeast corner of the field can be represented as , where , , and are positive integers with and relatively prime. Find .