Question

A man stands at a point A on the bank of a straight river, 1 mi wide. To reach point B, L = 4 mi downstream on the opposite bank, he first rows his boat to point P on the opposite bank and then walks the remaining distance x to B, as shown in the figure. He can row at a speed of 2 mi/h and walk at a speed of 5 mi/h. Find a function that models the time needed for the trip. And Where should he land so that he reaches B as soon as possible?

Answer 1

d = $Distce d rowed to point p is the hypotenuse :  \sqrt{1^2 + (4 -x )^2}    \sqrt{1 + 16 - 8x + x^2}      \sqrt{x^2 -8x + 17} Time to row distance at 2 mph     \sqrt{x^2 - 8x + 17}/2   total spent \sqrt{x^2 - 8x + 17}/2 + x/5$