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Math Help - Two Boats word problem - need function (please help)

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    Two Boats word problem - need function (please help)

    A boat leaves a dock at 2:00PM, and travels directly south at a speed of 20 miles per hour. Another boat is traveling towards the dock, from the west at a speed of 15 miles per hour. This boat will arrive at the dock at 3:00pm.


    a) write a function for the distance between the two boats in terms of x, where x = the amount of time (in hours) since 2:00pm.


    b) At what time were the two boats closest together?




    Thank you so much for any help you can give me.
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    Quote Originally Posted by Cwhitten85 View Post
    A boat leaves a dock at 2:00PM, and travels directly south at a speed of 20 miles per hour. Another boat is traveling towards the dock, from the west at a speed of 15 miles per hour. This boat will arrive at the dock at 3:00pm.


    a) write a function for the distance between the two boats in terms of x, where x = the amount of time (in hours) since 2:00pm.


    b) At what time were the two boats closest together?
    using t for time rather than x ...

    let the dock location be the origin

    position (x,y) of the first boat ... (0, -20t)

    position (x,y) of the second boat ... (15t-15, 0)

    distance formula ...

    d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

    distance between the two boats ...

    d = \sqrt{(15t-15)^2 + (20t)^2}

    graph the distance function to find the minimum.
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