1989 AIME Problem 6

Two skaters, Allie and Billie, are at points A^{}_{} and B^{}_{}, respectively, on a flat, frozen lake. The distance between A^{}_{} and B^{}_{} is 100^{}_{} meters. Allie leaves A^{}_{} and skates at a speed of 8^{}_{} meters per second on a straight line that makes a 60^\circ angle with AB^{}_{}. At the same time Allie leaves A^{}_{}, Billie leaves B^{}_{} at a speed of 7^{}_{} meters per second and follows the straight path that produces the earliest possible meeting of the two skaters, given their speeds. How many meters does Allie skate before meeting Billie?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.