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At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

  • math -

    Let the time past noon be t hours

    Distance, since noon, travelled by the westbound ship is 16t nautical miles, and ship B is 17t nautical miles.
    Let D be the distance between them
    D^2 = (16t)^2 + (17t)^2
    D^2= 545t^2
    D = (√545)t
    dD/dt = √545

    notice that dD/dt is a constant and independent of the time

    So the distance between them is constantly changing at √545 knots or 23.35 knots

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