Figuring Out Where to Land the Boat

A fisherman is out in his boat, a certain distance from the shoreline. He needs to come ashore, walk down the beach a bit, and then walk inland to his home. 

If a fisherman rows straight to shore, then walks along the beach until his home is the closest distance to the shoreline and walks inland, then he actually will have traveled farther than necessary. He probably will have taken more time than necessary, too. Aiming for a point down the shore to land his boat and then walking diagonally to his home will save time. 

The Problem Fisherman Fred is 3 miles off shore in his boat. His home is 19 miles down the shore and 8 miles inland. How much shorter is it to cut diagonally toward a point 4 miles down the beach and then travel diagonally from that point to his home  

Part IV Taking the Shape of Geometric Word Problems 

Two other considerations of taking a shorter route are the time that can be saved and the rates at which each leg of the journey are traveled. Some people can walk faster than they can row a boat, but others can really move through the water. Also, if the boat has a motor, then water travel may be the more efficient, but a bicycle or car can change the whole scenario. 

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