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Math Help - Story problem

  1. #1
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    Mar 2009
    From
    Rockford, Michigan
    Posts
    16

    Story problem

    BOAT
    .|
    .|2 Miles
    .|______________________
    .......4 miles of shoreline.....|
    .....................................| 1Mile
    .................................HOUSE
    Art rows @ 2 MPH and walks @ 4 MPH

    Art rowed to a point x miles down the shore towards his house and then walked directly to his house.

    I believe I have this part correct:
    Walking distance in terms of x: f(x) = sqrt of (4-x+1)
    Rowing distance in terms of x: f(x) = sqrt of (x^2+4)
    Time walking in terms of x: f(x) = sqrt of (4-x+1) all divided by 4
    Time rowing in terms of x: f(x) = sqrt of (x^2+4) all divided by 2

    Let me know if I'm OK so far.


    Write a function, T(x), for the total time it takes to get to Art's house from where he is located in the boat. Wouldn't I just add the last two functions together for the function for total time?
    Last edited by galanm; April 19th 2009 at 03:04 PM. Reason: 1 mile leg should be at the right end of the shore
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  2. #2
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    Quote Originally Posted by galanm View Post
    BOAT
    .|
    .|2 Miles
    .|______________________
    .......4 miles of shoreline.....|
    .....................................| 1Mile
    .................................HOUSE
    Art rows @ 2 MPH and walks @ 4 MPH

    Art rowed to a point x miles down the shore towards his house and then walked directly to his house.
    Assuming you mean x to stand for the distance between the ending of the direct line to shore (where you have the "2 Miles" line meet the horizontal line, above) and the point where the boat actually landed, then the Pythagorean Theorem (or the Distance Formula) should give you the following "distance" expressions:

    . . .boat:
    . . . . .sqrt[2^2 + x^2] = sqrt[4 + x^2]

    . . .land:
    . . . . .sqrt[(4 - x)^2 + 1^2] = sqrt[17 - 8x + x^2]

    Since d = rt, then t = d/r, so the "time" expressions will be:

    . . . . .boat: (sqrt[4 + x^2])/2
    . . . . .land: (sqrt[17 - 8x + x^2])/4

    Add the expressions for the two partial times to get an expression for the total time.

    Last edited by mr fantastic; April 19th 2009 at 11:23 PM. Reason: Reporting a bump is more efficient ....
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  3. #3
    Newbie
    Joined
    Mar 2009
    From
    Rockford, Michigan
    Posts
    16
    I see I forgot about squaring the 4-x. Thanks.
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