A vacationer on an island 8 miles offshore from a point that is 48 miles from town must travel to town occasionally. (See the figure.) The vacationer has a boat capable of traveling 40 mph and can go by auto along the coast at 65 mph. Island A beach, a town, an island, and a right triangle are drawn. The beach is represented by a horizontal line. The town is on the right end of the beach. 48 miles left of the town is a point on the beach, above which is the island 8 miles from the beach. A right triangle is formed by the 8 mile segment from the island to the beach, base of length x miles along the beach, and hypotenuse from the island going down and right to the beach. The right vertex of the triangle is 48 - x miles from town. Write an equation that represents the total time T (in hours) it takes for the vacationer to reach the town as a function of x, the point where the car is left. T(x) = Find T'(x). T'(X) = At what point should the car be left to minimize the time it takes to get to town? (Round your answer to one decimal place.) mi

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