A courier drives on a straight interstate highway at and then turns onto a dirt road…
MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A courier drives on a straight interstate highway at 60 mi/h and then turns onto a dirt road where the maximum speed is 30 mi/h. The courier starts at mile marker 0 on the highway (which runs east–west) and must reach a destination located 12 mi east of the starting marker and 12 mi south of the highway. The courier leaves the highway at a point x miles east of the start and then drives straight to the destination on the dirt road. Determine the value of x (to the nearest tenth of a mile) that minimizes the total travel time.