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Related rates question pls help

  1. Mar 22, 2008 #1
    A sailor in a boat 10 km off a straight coastline wants to reach a point 20km along the coast in the shortest possible time. Toward what point on the shore should he head if he can row at 4 km/h and run at 12 km/h?

    i believe this involves optomizeation as well ralated rates but i am unsure as to how to get the equasion to maximize.

    sailor ---------- | (straight coast)
    dx/dt=4 km/h |
    | y= 20 km dy/dt= 12 km/h
  2. jcsd
  3. Mar 22, 2008 #2
    srry guys, i tried to make a picture at the bottom. I didnt know it wouldn't permit the spaces i input.
  4. Mar 22, 2008 #3


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    Let x=0 be the point on the coast directly fronting the boat.

    Call the unknown point at the coas for X.

    Then, the time it takes for him to reach X by the boat is [itex]\frac{\sqrt{10^{2}+X^{2}}}{4}[/itex]
    and the time for him to reach his destination after that [itex]\frac{20-X} {12}[/itex]
    Thus, his total time T(X) is given by:
    [tex]T(X) =\frac{\sqrt{10^{2}+X^{2}}}{4}+\frac{20-X} {12}[/tex]
    Do you agree with this?
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