A graphing calculator is recommended A man stands at a point

A graphing calculator is recommended. A man stands at a point A on the bank of a straight river, 4 mi wide. To reach point B, 9 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. T(x) = Squareroot x^2-16x + 90/2 +x/5 Where should he land so that he reaches B as soon as possible () _________ miles from point B

Solution

x = dist from p to b
The distance (d) rowed to point p is the hypotenuse:
d = sqrt (4^2 + (9-x)^2)
d = sqrt (x^2 -18x +97)

Time to row this dist at 2 mph
t = sqrt (x^2 -18x+97)/2
Time spent walking at 5 mph = x/5
:
Total time (T): sqrt (x^2 -18x +97) + x/5

x = 8 mi; P to B (walking distance) Time rowing & walking; approx 5.72 hrs