Two cars are approaching an intersection. One is 2 miles south of the intersection and is moving at a constant speed of 30 miles per hour. At the same time, the other car is 3 miles east of the intersection and is moving at a constant speed of 40 miles per hour.

(a) Build a model that expresses the distance d between the cars as a function of time t.

At t = 0, the cars are 2 miles south and 3 miles east of the intersection, respectively.

(b) Use a graphing utility to graph d = d(t). For what value of t is d smallest?