At noon, ship a is 30 nautical miles due west of ship b. ship a is sailing west at 22 knots and ship b is sailing north at 23 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.)

We need to find relative speed between two ships. 
We look at relative speed along the north direction and west direction.

This is because boats are travaling at directions that are perpedincular to each other. Total relative speed is:

And that is how fast they are moving away from eachother.  
Please note that these boats are not accelerating, therefore the distance between them is increasing at the constant rate.