Your new house sits at a perpendicular distance of 6 miles

Last updated: 7/9/2022

Your new house sits at a perpendicular distance of 6 miles from the county highway across a flat parcel of land. The town where you work is 15 miles down the highway from that point P. You are going to build a gravel road that will connect somewhere to the county highway. The maximum speed on your gravel road will be 25 mph and the maximum speed on the county highway is 50 mph. You would like to be able to drive to town in the shortest time. a. Write the equation you will be working with in this problem. b. Use Calculus to determine how far down the highway from the point P you should connect your road to the county highway. C. How much time can be saved by constructing the road as you indicated in part b.