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Min/max problem

  1. Dec 6, 2006 #1
    1. The problem statement, all variables and given/known data
    A rower in a boat at a point P, 3km from the closest point Q on a straight shorline, wishes to reach a point r which is 5 km along the shoreline from Q. If he can row at 2km/h and walk at 4km/h along the shoreline, how far from point Q should the rower land the boat in order that the total time for the trip PR is minimized.



    3. The attempt at a solution

    Okay so if I let x be the distance from point Q, then the equation should be:

    t = 2(x^2+9)^(1/2) + 4(5-x)

    right?

    Then

    dt/dx = 2x/(x^2+9)^(1/2) - 4
    0 = 2x/(x^2+9)^(1/2) - 4
    4(x^2+9)^(1/2) = 2x
    (x^2+9)^(1/2) = 1/2x
    x^2+9 = 1/4x^2

    but that gives no solution.

    Could someone point me to where I went wrong please?
     
  2. jcsd
  3. Dec 7, 2006 #2

    AlephZero

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    Homework Helper

    Correct, the distance to row is sqrt(x^2+9) and the distance to walk is 5-x

    You got the times wrong. Speed = distance / time, not distance * time.
     
  4. Dec 7, 2006 #3

    HallsofIvy

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    Staff Emeritus
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    "Let x be the distance from Q to the point on the shoreline at which the boat lands" is much more infomative than "let x be the distance from point Q"!
     
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