? asked in Education & ReferenceHomework Help · 10 years ago

A boat can travel on a river 14 miles upstream in the same time it takes to travel 24 downstream. Find the spe?

A boat can travel on a river 14 miles upstream in the same time it takes to travel 24 downstream. Find the speed of the current if the speed of the boat in still water is 19 miles per hour.

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  • 10 years ago
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    the speed of boat in still water u = 19 mile/hour

    let the speed of the current = v mile/hour

    so

    speed of boat in up stream = u - v miles/ hour

    .......................................= 19 - v mile/ hour

    speed of boat in down stream = u+v mile/hour

    ...........................................= u - v mile/hour

    let the time taken be ' t ' in both cases

    distance traveled in upstream = 14 miles

    then t = 14 / ( u - v )

    => t = 14 / ( 19 - v ) ................ ( 1 )

    distance traveled in downstream = 24 miles

    then t = 24 / ( u + v )

    => t = 24 / ( 19 + v ) ..................( 2 )

    from equation ( 1 ) and ( 2 )

    14 / ( 19 - v ) = 24 / ( 19 + v )

    7 ( 19 + v ) = 12 ( 19 - v )

    133 + 7v = 228 - 12 v

    19v = 95

    => v = 5 mile/hour

    therefore speed of boat in still water = 5 mile/hour

  • 10 years ago

    time = distance / speed

    speed upstream = 19 - c (c = speed of current)

    time upstream = 14 / (19 - c)

    speed downstream: 19 + c

    time downstream = 24 / (19 + c)

    by inspection, the speed of the current is 5 mph, and the time traveled is 1 hour, but let's confirm that

    24 / (19 + c) = 14 / (19 - c)

    cross-multiply:

    14(19 + c) = 24(19 - c)

    266 + 14c = 456 - 24c

    38c = 190

    c = 190 / 38 = 5

    current is 5 mph

  • 3 years ago

    2. Six pears and 3 apples fee $3.ninety. 2 pears and 5 apples fee $3.30. How plenty does one pear fee? including the two: 8p + 8a = 7.20 => 1p + 1a = 0.ninety Subtraction => 4p - 2a = 0.60 => 2p - 1a = 0.30. including 3p = a million.20 => 1p = $0.40

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