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math

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Solve the problem. A cruise boat travels 48 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream.

  • math -

    Downstream: 48=(vb+vs)3
    upstsream: 46=(vb-vs)6
    multiply the first equation by 2
    1) 96=6vb+6vs
    2) 46=6vb-6vs
    subtract the equations:
    50=12vs solve for vs.

  • math still need help -

    i don't understand the way this is being worded. where did 46 come from? what does vs and vb stand for?

  • math -

    There is a mistake in bobpursley's equations - both should have the same distance of 48.

    vs = velocity of stream
    vb = velocity of boat
    and Distance = Velocity*Time

    Downstream
    48 = (vb + vs)*3
    The stream velocity is +ve as the time is shorter downstream - the stream helps
    So vb + vs = 16

    Upstream
    48 = (vb - vs)*6
    The stream velocity is -ve as the time is longer so the stream hinders the boat
    So vb - vs = 8

    Then just solve the 2 equations simultaneously to get vs = 4
    Check that and also find the velocity of the boat.

    I hope that helps.

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