A Vacationer on an Island 8 Miles Offshore from a Point

A vacationer on an island 8 miles offshore from a point that is 48 miles from a town to which the vacationer must travel occasionally. (See the figure.) The vacationer has a boat capable of traveling 30 mph and can go by auto along the coast at 55 mph. At what distance x from the point on shore closest to the vacationer on the island should the boat be left to minimize the time it takes to get to town? Round your answer to one decimal place. ​ Where , ​

A) ​6.1 miles
B) ​5.2 miles
C) ​5.9 miles
D) ​3.8 miles
E) ​4.3 miles

Correct Answer:

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