SOLUTION: 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

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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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%281%5E2%2Br%5E2%29
the time if he paddles at 3 km/h
%28sqrt%281%5E2%2Br%5E2%29%29%2F3
:
The distance he walks from point r to the campsite (Q):
(10-r)
the time if he walks at 5 km/h
%28%2810-r%29%29%2F5
:
Create an equation for the total time paddling and walking
T(r) = %28sqrt%281%5E2%2Br%5E2%29%29%2F3 + %28%2810-r%29%29%2F5
put this on your graphing calc, find the minimum time for some value of r

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