CALCULUS

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 19 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.)

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  1. After t hours, distance d is

    d^2 = (40+23t)^2 + (19t)^2
    2d dd/dt = 2(40+23t)(23) + 2(19t)(19)

    When t=5, d^2 = 155^2 + 95^2, d=181.8

    2(181.8) dd/dt = 2(155)(23) + 2(95)(19)
    363.6 dd/dt = 10740
    dd/dt = 29.5 knots

    check my math . . .

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  2. Your math be wrong.

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