A woman is standing at the edge of a slow-moving 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 8 miles downstream from the point directly across the river from the woman's starting point. What route will take the least amount of time? finish w m start 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 s 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 8 miles? (Leave your answer as a function of s.) Answer: s/3 I hr. (b) How long will it take her to walk wo miles? (Leave your answer as a function of t.) Answer: w/5 I hr. (c) Write the time it takes the woman to swim as a function of r. Answer: 1/3sqrt(1+x*2) I hr. (d) Use the fact that the campground is 8 miles downstream to write the time it takes the woman to walk as a function of c. Answer: w/'s I hr. (e) if I' denotes the total number of hours it takes the woman to swim s miles and then walk w miles, give a formula for T' as a function of ar, where a E [0, 8]. T(z) = (x)/(3son(1+2*2))-1/5 I hr. (f) Enter the critical number(s) of T(z). = 3/4 (g) How long will it take the woman to get to the campground if she takes the optimal route? Answer: 16/15 I hours