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A boat travel 4 miles upstream with a current of 5 miles per hour. It takes 40 mminutes longer to go upstream. How fast does the boat go downstream

  • algebra -

    They probably expect you to assume that the boat is using the same power to go through the water in both directions.

    Let V be the boat speed relative to the water in both directions. Relative to the shore, its speed is V+5 going downstream and V-5 going upstream.

    Let T be the time that it takes to go downstream, in hours. It take T + 2/3 to go upstream. You can write two equations in the two unknowns, V and T.

    4 = (V+5) T
    4 = (V-5)(T + 2/3)

    4 = (V-5)[4/(V+5) + (2/3)]
    4(V+5) = 4(V-5) + (2/3)(V^2-25)
    40 = (2/3)(V^2-25)
    V^2-25 = 60
    V^2 = 85
    V = 9.22 mph.
    Downstream speed = 14.22 mph
    Upstream speed = 4.22 mph
    Dowstream travel time = 4/14.22
    = 0.281 hrs = 16.9 minutes
    Upstream travel time = 4/4.22 = 0.948 hr = 56.9 min

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