Results 1 to 1 of 1

Math Help - Am I on the right track?

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    Canada
    Posts
    3

    Am I on the right track? - Solved.

    A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 11 miles down the shore from P in the least time?

    She must row a distance of : \sqrt{x^2 + 16}
    She must walk a distance of : 11-x

    t=\frac{d}{t}

    The time traveled over water plus the time traveled over land can be written:

    \frac{\sqrt{x^2 + 16}}{3} + \frac{11-x}{4}

    If this is correct, how would I find the derivative of the above function..?
    Would this be the derivative?

    T^'  (x) = \frac{x}{3\sqrt{x^2 + 16}} - \frac{1}{4}

    Finding a common denomenator:

    \frac{4x-3\sqrt{x^2 + 16}}{12\sqrt{x^2 + 16}} ?


    -----------------------------------------------------------

    I figured out the solution myself. If anyone is curious to how I solved it, here is what I did:


    4x-3\sqrt{x^2 +16} = 0
    x = \frac{12}{\sqrt{7}}

    From here I plugged in 0, 11, and \frac{12}{\sqrt{7}} back into my original equation. I found that \frac{12}{\sqrt{7}} was the minimum time that occured at the stationary point. Therefore, she would land the boat \frac{12}{\sqrt{7}} miles down the shore from point P.
    Last edited by aprilsauce; March 10th 2013 at 02:14 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Am I on the right track.
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: December 4th 2010, 01:20 PM
  2. Right track?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 4th 2010, 12:38 PM
  3. Am I on the right track?
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: February 18th 2010, 02:49 PM
  4. Am I on the right track?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 30th 2009, 04:17 AM
  5. Am I on the right track here??
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 10th 2008, 12:02 PM

Search Tags


/mathhelpforum @mathhelpforum