A woman is standing at the edge of a slowmoving river which is one mile wide, and she wishes to return to her campground on the opposite side of the river. Assume that the woman can walk at 5 miles per hour and swim at 3 miles per hour, and that she will first swim to cross the river and then walk the remaining distance to the campground, which is 7 miles downstream from the point directly across the river from the woman's starting point. What route will take the least amount of time? start Click on the graph to open it in a new window. See the diagram for the following: The woman's starting location is marked with a red 'X', her ending location is marked with a yellow star, and one of the possible routes for her is marked with a red solid line. The variable 5 denotes the distance (in mi) that she will swim, and the variable w denotes the distance (in mi) that she will walk, i.e., the distance between the red and blue arrows. Let x denote the distance (in mi) between the black and red arrows. (a) How long will it take her to swim 3 miles? (Leave your answer as a function of 5.) Answer: 2 hr. (b) How long will it take her to walk w miles? (Leave your answer as a function of w.) Answer: 2 hr. (c) Write the time it takes the woman to swim as a function of x. Answer: 2 hr. (d) Use the fact that the campground is 7 miles downstream to write the time it takes the woman to walk as a function of x. Answer: 2 hr. (e) If T denotes the total number of hours it takes the woman to swim 5 miles and then walk w miles, give a formula for T as a function of x, where x E [0, 7]. T(x) = 2 hr. (f) Enter the critical number(s) of T(x). x = E (9) How long will it take the woman to get to the campground if she takes the optimal route? Answer: 2 hours