Results 1 to 3 of 3

Math Help - Optimization problem (not sure if I understand correctly)

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    119

    Optimization problem (not sure if I understand correctly)

    A man in a boat is 3 km offshore and wishes to go to a point on the shore that is 5km from the point that is directly opposite his present position. The man can walk at 4 km/h and row at 2 km/h. At what point should he land so as to reach his destination in the shortest time? What is the traveling time?

    I set up the equation as follow \displaystyle d(t)=\sqrt{(3-2t)^2 + (5-4t)^2}

    Differentiating and found a local minimum at x=\frac{10}{13}

    However, the answer in supposedly 3.27 km, 2.55 hours.

    What am I doing wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,696
    Thanks
    450
    Quote Originally Posted by youngb11 View Post
    A man in a boat is 3 km offshore and wishes to go to a point on the shore that is 5km from the point that is directly opposite his present position. The man can walk at 4 km/h and row at 2 km/h. At what point should he land so as to reach his destination in the shortest time? What is the traveling time?

    I set up the equation as follow \displaystyle d(t)=\sqrt{(3-2t)^2 + (5-4t)^2}

    Differentiating and found a local minimum at x=\frac{10}{13}

    However, the answer in supposedly 3.27 km, 2.55 hours.

    What am I doing wrong?
    did you make a sketch?

    first off, you're minimizing time.

    time = \frac{distance}{speed}

    t_{total} = \dfrac{\sqrt{x^2+9}}{2} + \dfrac{5-x}{4}

    set \dfrac{dt}{dx} = 0 and find the value of x that minimizes t.


    btw ... don't bump.
    Attached Thumbnails Attached Thumbnails Optimization problem (not sure if I understand correctly)-boatprob.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2010
    Posts
    119
    Quote Originally Posted by skeeter View Post
    did you make a sketch?

    first off, you're minimizing time
    Ahh, that's what I was missing. Thanks a lot for your help!

    Sorry about the bumping, won't happen again.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Have I done this 'show that' problem correctly?
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: July 10th 2010, 06:59 AM
  2. Replies: 3
    Last Post: April 12th 2010, 04:03 AM
  3. Did I do this problem correctly... simplifying logs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 17th 2009, 11:17 AM
  4. Replies: 1
    Last Post: November 15th 2009, 05:07 PM
  5. Did I do this problem correctly?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 27th 2007, 11:06 PM

Search Tags


/mathhelpforum @mathhelpforum