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26 April, 04:32

Two boats leave a port at the same time. one travels west at 20 mph, and the other travels south at 15 mph. how fast is the distance between them changing after 2 hours?

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  1. 26 April, 05:54
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    Let's define variables:

    x: boat travels west

    y: boat travels south

    d: distance between boats.

    Using the Pythagorean theorem we have:

    d ^ 2 = x ^ 2 + y ^ 2

    Where,

    x = 20 * 2 = 40 miles

    y = 15 * 2 = 30 miles

    d = root ((40) ^ 2 + (30) ^ 2) = 50 miles

    We now derive the equation with respect to time:

    2dd ' = 2xx' + 2yy '

    We cleared d ':

    d ' = (2xx' + 2yy ') / (2d)

    Substituting values:

    d ' = (2 * (40) * (20) + 2 * (30) * (15)) / (2 * (50))

    d ' = 25 mph

    Answer:

    the distance between them is changing at 25mph after 2 hours
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