Calculating how fast distance changes between ships

[hsd]

Homework Statement

At noon, ship A is 50km west of ship B. Ship A is sailing south at 30km/h and ship B is sailing north at 20km/h. How fast is the distance between the ships changing at 4:00pm in km/h.

Homework Equations

The Attempt at a Solution

http://img822.imageshack.us/img822/2420/shipq2.png

but the final answer is coming out wrong

 

[haruspex]

I don't understand the very first line of your answer. Why are you taking the squares of the velocities? Where is the 50km in this? If you substitute t = 0 in your equation, what number should you get?

 

[AJ Bentley]

Ship A is heading south at 30 for 4 hours so travels 120 km. Similarly B travels 80 due north.
So they become separated by 200km north/south.
They are separated by 50 km due east west to begin with.

So the distance between the ships is? (pythagoras).
The angle of the same triangle is also the direction cosine of the motion so you can use that to calculate their mutual speed.