Results 1 to 4 of 4

Math Help - Related Rates word problem

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    4

    Related Rates word problem

    I think it's a related rates problem. Anyway, I'm totally stumped on this problem and any help would be appreciated.

    A man, who is in a boat 2 miles from the nearest point A on a straight shoreline, wants to reach a house located at point B which is 6 miles further down the coast. He plans to row to point P that is between point A and B. P is also x miles from the house. He will then walk the remainder of the distance to the house. Suppose he can row at a rate of 3 mph. He can walk at a rate of 5 mph. If T is the total time to reach the house, express T as a function of x.

    Here's a (horrible) picture I drew:http://i81.photobucket.com/albums/j2...key/lolwut.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member roy_zhang's Avatar
    Joined
    Mar 2008
    Posts
    64
    Let's say your start point is S, according to your picture, we have SP = \sqrt{(6-x)^2+2^2}=\sqrt{x^2-12x+40}.

    So your time spend on the river is \frac{\sqrt{x^2-12x+40}}{3} and your time spend on land is \frac{x}{5}

    Hence total time (in hours) can be expressed as T(x)=\frac{\sqrt{x^2-12x+40}}{3}+\frac{x}{5}

    From here I guess you can answer the question like: determine the distance x such that you can reach the house in minimum amount of time.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,548
    Thanks
    539
    Hello, bob9171!

    This is a classic problem, found in every Calculus text.


    A man, in a boat 2 miles from the nearest point A on a straight shoreline,
    wants to reach a house located at point B which is 6 miles further down the coast.
    He plans to row to point P that is between point A and B.
    P is also x miles from the house.
    He will then walk the remainder of the distance to the house.
    Suppose he can row at a rate of 3 mph and can walk at a rate of 5 mph.
    If T is the total time to reach the house, express T as a function of x.
    Code:
        M *
          | *
          |   *
        2 |     *
          |       *
          |         *
          * - - - - - * - - - - - - *
          A    6-x    P      x      B

    We are told that: . MA = 2,\;A = 6,\;x =PB
    . . Hence: . AP = 6-x


    From the right triangle MAP:\;\;MP \:=\:\sqrt{(6-x)^2 + 2^2}\:=\:\sqrt{x^2-12x + 40}
    He rows that distance at 3 mph.
    . . This takes him: . \frac{\sqrt{x^2 - 12x + 40}}{3} hours.

    Then he walks x miles at 5 mph.
    . . This takes him: . \frac{x}{5} hours.

    His total time is: . T \;=\;\frac{\sqrt{x^2-12x+40}}{3} + \frac{x}{5} . hours.


    Edit: Too fast for me, Roy!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2007
    Posts
    4
    Well that was pretty simple. Thanks a bunch!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. related rates word problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 10th 2013, 02:01 PM
  2. Related Rates Word Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 27th 2011, 06:08 PM
  3. related rates word problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 28th 2010, 07:44 PM
  4. Related Rates Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 14th 2009, 05:01 AM
  5. Related Rates Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 4th 2009, 12:04 PM

Search Tags


/mathhelpforum @mathhelpforum