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A boat goes 48 miles downstream with the current in 3 hours and returns upstream against the current in 4 hours. Find the rate of the boat in still water and rate of the current flow.

Please show work so I can understand. Thanks!

3 Answers

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  • Anonymous
    8 years ago
    Favorite Answer

    b = boat speed

    c = current speed

    b + c = 48mi/3hr = 16mi/hr

    b - c = 48mi/4hr = 12mi/hr Solve this one for b and substitute that into the first equation.

    b = 12 + c

    12 + c + c = 16

    2c = 4

    c = 2 mi/hr Plug this value into either equation and solve for b.

    b + 2 = 16

    b = 14 mi/hr

  • 8 years ago

    A boat goes 48 miles downstream with the current in 3 hours and returns against the

    current in 4 hours. Find the rate of the boat in still water and rate of the current flow.

    S = D/T

    S = speed in mph

    D = distance in miles

    T = time in hours

    Downstream

    Sd = 48 mi/3 hr = 16 mph

    D = ST

    D = 16(3) = 48

    (Sb + Sc) = 16

    Sc = 16 - Sb

    Upstream

    Su = 48 mi/4 hr = 12 mph

    D = ST

    D = 12(4) = 48

    (Sb - Sc) = 12

    Sb = 12 + Sc

    Sb -12 = Sc

    Sc = Sb - 12

    16 - Sb = Sb - 12

    16 = 2Sb - 12

    16 + 12 = 2Sb

    28 = 2Sb

    2Sb = 28

    Sb = 28/2 = 14 mph Speed of boat in still water

    Downstream

    Sc = 16 - Sb

    Sc = 16 - 14 = 2 mph Speed of current

    Upstream

    Sc = Sb - 12

    Sc = 14 - 12 = 2 mph Speed of current

  • 8 years ago

    b + c = 16 mi/hr

    b - c = 12 mi/hr

    ________________add

    2b = 28 mi/hr

    b = 28/2 = 14 mi/hr <<rate of the boat in still water

    using the first equation:

    14 + c = 16

    c = 16 - 14 = 2 mi/hr <<rate of current flow

    check using the second equation:

    14 - 2 = 12

    12 = 12

    - .--

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