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How would I write a equation for this and solved?

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The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?

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  1. X = 60

    Vu= 57mph

    Vd= 63mph

    X = V*t

    upriver

    60 = (V–3)t

    t = 60/(V–3)

    downriver

    60 = (V+3)(9–t)

    combined:

    60 = (V+3)*(9–(60/(V–3)))

    times everything by V–3

    60V–180 = (V+3)(9V–27–60)

    60V–180 = 9V^2 + 27V –87V–261

    0 = 9V^2 –120V – 81

    0 = 3V^2 –40V – 27

    Quad Formula:

    V = (40 + √(1924))/6 = (20+√(481))/3

    ~13.977  


  2. In running water:

    The boat travels a distance of 60 miles up. It take him 9 hours to reach there. That means, he is traveling at a speed of 60 miles per 9 hours. Or, 60/9 = 6 2/3 miles per hour. Notice that the river is flowing down and pushing him backwards since he wants to go up.The river is pushing him down at a speed of 3 miles per hour. That means actually, he is going at a speed of 9 2/3 miles per hour, but the river is slowing him down by 3 miles per hour, so that he is only moving at a speed of 6 2/3 miles per hour.

    If the water is not moving and doesn't pull him down, he will be traveling at 9 2/3 miles per hour. END

    The equation can be: S = (D / T) - R

    where,

    S means the speed of the boat,

    D means the distance to travel

    T means the time taken

    R means the speed at which the river is pushing him down

    If the water is still, R = 0.

  3. time1= 60/(r+3)

    time2= 60/(r-3)

    time1+time2 = 9 hrs

    Answer: 13.977237 mi/hr

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