Related Rates problem

[q_fruit]

Q:
Boat A is travelling due north at 16 miles per hour. At 7 AM boat B, 20 miles due north of A, is travelling due east at 18 miles per hour. At 7:30 AM is the distance between them decrasing or increasing and at what rate?

Okay, so I'm trying to figure out what variables I know and trying to draw a diagram using a triangle, but I'm a little confused...

Am I right with this? :

y=20 mi
dy/dt=16 mi/hr
dx/dt=18 mi/hr
so we need to know, x=?, z=?, and dz/dt=?

Thanx.

 

[pka]

\(\displaystyle \L
z^2 = \left( {20 - x} \right)^2 + y^2\)

\(\displaystyle \L
2z\frac{{dz}}{{dt}} = - 2(20 - x)\frac{{dx}}{{dt}} + 2y\frac{{dy}}{{dt}}\)

\(\displaystyle \L
x = 8\quad \& \quad y = 9\quad \Rightarrow \quad z = 15\)

 

[q_fruit]

Why do you do 20-x?

 

[pka]

THINK ABOUT IT!
Boat A is going north to B.

 

[q_fruit]

I am thinking.. I thought the distance between A and B is 20 miles, while the rate A is travelling is 16 miles/hour. Maybe I'm missing something here but I don't understand why you're subtracting x from 20.
The last time I did these problems were months ago and I'm trying to refresh my memory by doing this, so sorry if I'm slow.

 

[pka]

A starts 20mi south of point B. It sails north.
If A goes x miles, then there (20−x) miles between A and point B.
Boat b sails y miles to the east.
So the distance between the two boats is z.
The length z is the hypotenuse of a right triangle with legs y & (20−x).