US ANSWERS SCALCET8 4.7.049. MY NOTES PRACTICE ANOTHER A man launches his boat from point A on a bank of a straight river, 4 km wide, and wants to reach point B, 3 km downstream on the opposite bank, as quickly as possible (see the figure below). He could row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row 6 km/h and run 8 km/h, where should he land to reach B as soon as possible? (We assume that the speed of the water is negligible compared to the speed at which the man rows. ) (Hint: This question is based on EXAMPLE 4 in Section 4.7 of the textbook. However, for this question, the textbook has added a challenge which may require an unexpected solution. Look for it!) 4.536 x km from C C D Enhanced Feedback Please try again and draw a diagram. Keep in mind that t = , where t is time, d is the distance, and r is the rate. Let x be the distance between C and D. Use the Pythagorean theorem to find the distance between A and D. Write a function for the time the man travels from point A to D and then to B. Use calculus to find x such that the time is minimized