Question 578988
A man is on a lake in a canoe one kilometer from the closest point P of a straight shore line.
 He wishes to get to his campsite at point Q, 10 kilometers along the shore form point P.
 In order to accomplish this, he paddles to point R between P and Q then walks the remaining distance to Q.
 He can paddle 3 km/hr and walk 5 km/hr.
How should he pick the ponit R so as to get to Q as quickly possible?
:
let r = the distance from point p 
the distance he paddles will be the hypotenuse of a triangle formed by 1 kr and r
{{{sqrt(1^2+r^2)}}}
the time if he paddles at 3 km/h
{{{(sqrt(1^2+r^2))/3}}}
:
The distance he walks from point r to the campsite (Q):
(10-r)
the time if he walks at 5 km/h
{{{((10-r))/5}}}
:
Create an equation for the total time paddling and walking
T(r) = {{{(sqrt(1^2+r^2))/3}}} + {{{((10-r))/5}}}
put this on your graphing calc, find the minimum time for some value of r
{{{ graph( 300, 200, -2, 5, -1, 3, (sqrt(1+x^2)/3)+((10-x)/5)) }}} 
the distance r is from the point p is on the x axis
the total time is on the y axis
Mimimum time is when, point r is .75 km from p and 9.25 km from Q