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Math Help - Speed of Boat in Still Water

  1. #1
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    Speed of Boat in Still Water

    Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4 mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?

    MY WORK:

    Let A = against the current

    Let W = with the current

    The boat will travel faster with the current and slower against the current. Is this correct?

    Here is my set up:

    ...........rate..........time........distance
    A.......(x+4).....(x + 20)........(x+4)(x+20)
    W.......(x-4).......(x)..............(x-4)(x)

    Since the distance she travelled both ways is the same, I set up the following equation:

    (x+4)(x+20) = (x-4)(x)

    The letter x here represents the speed of the boat in still water.


    Is any of this correct?

    If not, what did I do wrong?




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  2. #2
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    distance = velocity \times time

    Let t = time taken to travel downstream.
    Let v = the velocity of the boat in still water.

    using d = vt,

    5 = (v - 4) \times (t + 20)

    5 = (v + 4) \times t

    We want 'v' on its own so we can solve, so divide the 'v parts' across to the other side.

    \frac{5}{v-4} = t + 20

    \frac{5}{v+4} = t

    \frac{5}{v - 4} = \frac{5}{v+4} + 20

    Multiply whole expression by (v + 4)(v - 4)

    5(v + 4) = 5(v - 4) + 20(v + 4)(v - 4)

    Now simplify and solve the quadratic formed.

    Don't hesitate to ask for further help...
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  3. #3
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    ok..........

    Quote Originally Posted by nzmathman View Post
    distance = velocity \times time

    Let t = time taken to travel downstream.
    Let v = the velocity of the boat in still water.

    using d = vt,

    5 = (v - 4) \times (t + 20)

    5 = (v + 4) \times t

    We want 'v' on its own so we can solve, so divide the 'v parts' across to the other side.

    \frac{5}{v-4} = t + 20

    \frac{5}{v+4} = t

    \frac{5}{v - 4} = \frac{5}{v+4} + 20

    Multiply whole expression by (v + 4)(v - 4)

    5(v + 4) = 5(v - 4) + 20(v + 4)(v - 4)

    Now simplify and solve the quadratic formed.

    Don't hesitate to ask for further help...
    Thank you. I can take it from here.
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