Two robots start in opposite corners of a square arena, 150 feet on a side. They each move along a straight path toward a goal that is 112.5 feet east and 75 feet north of the southwest corner. Robot A, starting in the northwest corner, moves so that each second it is two feet south and three feet east of its previous position. Robot B moves so that each second it is two feet west and four feet north of its previous position.
a. Using the southwest corner of the arena as the origin, write parametric equations for the paths of the robots in terms of the number of seconds.
b. Which robot reaches the goal first? How far away is the other robot?
