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At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 20 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

  • calculus -

    let t hours be some time past 12:00 noon

    After t hours, ship B has gone 20t knots
    and ship A has gone 17t knots

    let the distance between them be D
    I see a right-angled triangle and
    D^2 = (20t)^2 + (17t+10)^2
    D^2 = 689t^2 + 340t + 100
    2D(dD/dt) = 1378t + 340
    dD/dt = (689t + 170)/D

    at 4:00 pm, t=4 and
    D^2 = 12484
    D = 111.7318

    so at t=4
    dD/dt = (689(4) + 170)/111.7318
    = 26.19 knots

  • calculus -

    It still says NOT CORRECT.

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