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

At , the cars are miles south and miles east of the intersection, respectively.

Draw the related diagram.

A is moving at a constant speed of miles per hour.

B is moving at a constant speed of miles per hour.

If is in hours, is the distance travelled with the speed mph at time .

is the distance travelled with the speed mph at time .

The distance from car A to the intersection is .

The distance from car B to the intersection is .

Apply Pythagorean theorem, .

.

**(b)**

Graph the function .

Locate the minimum point on the graph.

is smallest when hr.

**(a)** .

**(b)** is smallest when hr.

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