Solved: Athletics An athlete has set up a course for training as part of her regimen in

Chapter 0, Problem 69

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Athletics An athlete has set up a course for training as part of her regimen in preparation for an upcoming triathlon. She is dropped off by a boat 2 miles from the nearest point on shore. The finish line is 4 miles down the coast and 2 miles inland (see figure). She can swim 2 miles per hour and run 6 miles per hour. The time (in hours) required for her to reach the finish line can be approximated by the model where is the distance down the coast (in miles) to the point at which she swims and then leaves the water to start her run. (a) Find the times required for the triathlete to finish when she swims to the points and miles down the coast. (b) Use your results from part (a) to determine the distance down the coast that will yield the minimum amount of time required for the triathlete to reach the finish line. (c) The expression below was obtained using calculus. It can be used to find the minimum amount of time required for the triathlete to reach the finish line. Simplify the expression.