Question 249420
A man stands at a point A on the bank of a straight river, 2 mi wide.
 To reach point B, 7 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.
 He can row at a speed of 2 mi/h and walk at the speed of 5 mi/h.
 Where should he land so that he reaches B as soon as possible?
:
x = dist from p to b
The distance (d) rowed to point p is the hypotenuse:
d = {{{sqrt(2^2 + (7-x)^2)}}}
d = {{{sqrt(4 + 49 - 14x + x^2)}}}
d = {{{sqrt(x^2 - 14x + 53)}}}
Time to row this dist at 2 mph
t = {{{(sqrt(x^2 - 14x + 53))/2}}}
:
Time spent walking at 5 mph = {{{x/5}}}
:
Total time (T): {{{(sqrt(x^2 - 14x + 53))/2}}} + {{{x/5}}}
:
Graph this and find the minimum time
{{{ graph( 300, 200, -6, 20, -5, 6, (sqrt(x^2 - 14x + 53))/2 + (x/5) ) }}}
:
x = 6.1 mi; P to B (walking distance) Time rowing & walking; approx 2.3 hrs