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Math Help - Motorboat

  1. #1
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    Motorboat

    A motorboat can go 16 miles downstream in 20 minutes. It takes 30 minutes for this same baot to go upstream the same 16 miles.

    Let x = the speed of the boat.
    Let y= the speed of the current.

    a. Write an equation for the motion of the motorboat downstream.
    b. Write an equation for the motion of the motorboat upstream.
    c. Find the speed of the current.

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  2. #2
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    Let d = 16 miles
    Let t_d = 20 minutes
    Let t_u = 30 minutes

    The speed of the boat when it goes downstream is x+y
    Therefore \frac{d}{x+y} = t_d
    Inverse gives (i) \frac{x}{d} + \frac{y}{d} = \frac{1}{t_d}

    The speed of the boat when it goes upstream is x-y
    Therefore \frac{d}{x-y} = t_u
    Inverse gives (ii) \frac{x}{d} - \frac{y}{d} = \frac{1}{t_u}

    Equation (i) - equation (ii) gives
    2 \frac{y}{d} = \frac{1}{t_d} - \frac{1}{t_u}

    y = \frac{d}{2} (\frac{1}{t_d} - \frac{1}{t_u})

    y = 8 mph
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  3. #3
    Member Greengoblin's Avatar
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    v=\frac{s}{t}

    x+y=\frac{16}{20}

    x-y=\frac{16}{30}

    Then you have two simultaneous equations to solve.
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  4. #4
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    ok....

    Quote Originally Posted by running-gag View Post
    Let d = 16 miles
    Let t_d = 20 minutes
    Let t_u = 30 minutes

    The speed of the boat when it goes downstream is x+y
    Therefore \frac{d}{x+y} = t_d
    Inverse gives (i) \frac{x}{d} + \frac{y}{d} = \frac{1}{t_d}

    The speed of the boat when it goes upstream is x-y
    Therefore \frac{d}{x-y} = t_u
    Inverse gives (ii) \frac{x}{d} - \frac{y}{d} = \frac{1}{t_u}

    Equation (i) - equation (ii) gives
    2 \frac{y}{d} = \frac{1}{t_d} - \frac{1}{t_u}

    y = \frac{d}{2} (\frac{1}{t_d} - \frac{1}{t_u})

    y = 8 mph
    What a great detailed reply! Thank you for your time and effort.
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  5. #5
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    ok.....

    Quote Originally Posted by Greengoblin View Post
    v=\frac{s}{t}

    x+y=\frac{16}{20}

    x-y=\frac{16}{30}

    Then you have two simultaneous equations to solve.
    I thank you for your time and effort.
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