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At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

  • Math! -

    I assume you made a diagram.

    let the time passed since noon be t hours
    in that time ship A has traveled 25t n-miles , and ship B has traveled 16t n-miles
    let the distance between them be d n-miles

    I see a right-angled triangle with base of
    50 + 25t, a height of 16t and a hypotenuse of d

    d^2 = (50+25t)^2 + (16t)^2
    at 6:00 pm, t = 6
    d^2 = 221.847

    2d(dd/dt) = 2(50+25t)(25) + 2(16t)(16)

    so at 6:00 pm
    dd/dt = [2(50+150)(25) + 2(96)(16)]/221.847
    = 58.923

    check my arithmetic

  • Math! -

    This answer isn't right either & I don't understand how you got d^2 = 221.847.

  • Math! -

    that d^2 = 221.847 was a typo

    should have said d = 221.847
    As you can see further down I used it as such.

    Alos in my third last line of my previous post I should have divided by 2(221.847) to get
    29.46 instead of 58.923

  • Math! -

    Yeah. That's better. Thanks again!

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