Rate of change in distance question

[Dr Zoidburg]

Okay, I'm 99% sure I've got the right answer here, but I just wanted to make certain before I send my assignment in. It's the last question and has been bugging me for the last few days until I had an eureka moment just a few minutes back.
(In case you're wondering, I'm doing my studies by correspondence, so other than course notes and textbooks borrowed from the library I have just the internet and my brains (hah!) to aid me)

Homework Statement

A baseball diamond has sides 27m long. A player is running from 2nd to 3rd at a speed of 9m/s. When he is 6m away from 3rd, at what rate is the player's distance from home plate changing at that instant?

The Attempt at a Solution

x = distance from home plate to 3rd = 27m
y = distance from player to 3rd = 6m
z = distance from player to home = 27.66m (using pythagoras)
speed of player is change of y over time: dy/dt = 9m/s

$$z^{2}$$ - $$y^{2}$$= $$x^{2}$$
differentiate with respect to time:
d/dz$$z^{2}$$ - d/dy$$y^{2}$$= 0 (since x doesn't change over time)

dz/dt*2z - dy/dt*2y = 0
divide by 2:
z*dz/dt - y*dy/dt = 0
sub the above (z, y, dy/dt) into the equation and solve:
dz/dt = 1.95m/s

If this ain't correct, please tell me quickly as I need to post my assignment off asap!

 

[tiny-tim]

Hi Dr Zoidburg!

Yes, that's fine (but a little messy)!

Try shortening it a bit.

For example, there's no need to define an x (I know it's useful for helping you get to your eureka moment, but once you're there, you can forget it) … just say z² = y² + 729 (or z = √(y² + 729)).

And

d/dz$$z^{2}$$ - d/dy$$y^{2}$$= 0

doesn't make sense, does it?

 

[Dr Zoidburg]

yay, got it right! Off to the post office I scurry.

And that other bit just came out poorly due to bad formating. It looks better in my assignment

 

[tiny-tim]

yay, got it right! Off to the post office I scurry.

I thought Dr Zoidburg scuttled ? ​

 

[Dr Zoidburg]

whoops. you're right there. scuttled. whoop! whoop! whoop!

"Friends, help! A guinea pig tricked me!"

 

[tiny-tim]

I just did a google search for "A guinea pig tricked me",

and got 5370 hits! ​