Question

Grades Achievements Course Help (1 point) 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 10 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 1 mi S start Click on the graph to open it in a new window. See the diagram for Die 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 variables 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 s miles? (Leave your answer as a function of s.) Answer: 2 hr. (b) How long will it take her to walk w miles? (Leave your answer as a function of w.) Answer:

Answer 1

Solution Given, Walking speed (VW) = 5 mil hours Swimming speed (Vs) - 3 mil hours And x + W = 10 miles a) Time taken to swim 's miles -s/Velocity s ho Vs 3 ts ho دوای b) Time taken to walk 'w'miles vo ho tw ठी c) According to Pythagorus theorem, x2 1? 32 = √ xc ²+1 S. S. ts Jx²+1 3 hr. Since, xtw = 10 - w=10-0² So 10-x to tw = at Total time to reach destination tetto

+ Ос 5 cho To minimize time, but IT Ix d 4 2 - 1 1. x .35x²ī ajeni = ) 500 On 1 35x²+1 squaring we gel (5 se je = g(x+1) 16x²-9=0 -> (42-3)(43c + 3) = 0 2 ve E [0,1]) or, x = 0.75 miles 1 3 ) T(x = 0.76) √(0.75)²+1 +2 - 0.75 5 3 = 1 +1.25 +1.85 3 = 2.267 hours. Hence, optimal route take 2.267 hours