math
posted by bob dylan .
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.)

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