At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west

Question

At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 24 knots and ship B is sailing north at 20 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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Note: Draw yourself a diagram which shows where the ships are at noon and where they are "some time" later on. You will need to use geometry to work out a formula which tells you how far apart the ships are at time t, and you will need to use "distance = velocity * time" to work out how far the ships have travelled after time t.

Explanation / Answer

D=sqrt(x^2+y^2) dD/dt=1/2sqrt(x^2+y^2)*(2dx/dt+dy/dt)

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