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Maximum and Minimum Distance Word Problem

Johnny Steamboat wants to sail from his island home to town in order to purchase a book of carpet samples. His home island is 7 miles from the nearest point on the shore. The town is 35 miles downshore and one mile inland. If he can run his steamboat at 12 mph and catch a cab as soon as he reaches the coast that will drive 60 mph (a 4x4 that drives in a straight line cross country).
How far down the coast should Johnny land in order to minimize the time it takes to get to town?

Solution Summary

A maximium/minimum distance problem is solved. The solution is detailed and well presented. A diagram is included.