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Homework Help: Optimization -writing and solving the equations

  1. Dec 12, 2009 #1
    Hi
    Im trying to write an equation for the question below. Could someone please point me in the right direction with writing it?
    1. The problem statement, all variables and given/known data

    An island is 4km from the nearest point p on the straight shoreline of a lake. if a person can row a boat at 3km/h and walk at 5km/h where should the boat be landed to arrive at a town 10km away is the least time?

    2. Relevant equations



    3. The attempt at a solution
    I think the equation is y=(1/3)*(4^2+x^2)^(1/2)+((10-x)/5)

    this doesn't look hard to differentiate but i cant seem to get the right answer-
    in fact i get imaginary numbers

    this is what i did

    y=(1/3)*(16+x^2)^(1/2)-(1/5*x)+2
    y'= -1/5+1/2*1/3(16+x^2)^(1/2)*2x
    y'= -1/5+(2x/(6(16+x^2)^(1/2))
    y'=0
    1/5=x/(3(16+x^2)^(1/2))
    3*(16+x^2)^(1/2)=5*x //square both sides
    9*(16+x^2)=5*x^2
    144+9x^2-5x^2=0
    x= +/- 6i //this is obviously wrong as a person does not travel imaginary distances
     
  2. jcsd
  3. Dec 12, 2009 #2

    tiny-tim

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    Homework Helper

    Welcome to PF!

    Hi Poppynz! Welcome to PF! :smile:

    (have a square-root: √ and try using the X2 tag just above the Reply box :wink:)
    oops! :redface: … you forgot to square the 5, so you got 5 - 9 instead of 25 - 9 :rolleyes:

    Try again! :smile:
     
  4. Dec 12, 2009 #3
    haha such a silly mistake thanks :)
     
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