algebra

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A boat can travel 114 miles upstream
in the same time that it can travel 186 miles downstream.
If the speed of the current is 6 miles per hour,
find the speed of the boat without a current.

  • algebra -

    any help would be greatly appreciated :)

  • algebra -

    Speed of boat in still water = V mi/h.

    Speed of boat upstream = V-6 mi/h.

    Speed of boat down stream = V+6 mi/h.

    (V-6)t = 114 mi.
    Eq1: Vt - 6t = 114.

    (V+6)t = 186 mi.
    Eq2: Vt + 6t = 186.

    Add Eq1 and Eq2 and get:
    2Vt = 300,
    Vt = 150.

    In Eq1, substitute 150 for Vt:
    150 - 6t = 114,
    -6t = 114 - 150 = -36,
    t = 6h.

    In Eq2, substitute 6 for t:
    6V + 6*6 = 186,
    6V + 36 = 186,
    6V = 150,
    V = 25mi/h.

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