Calculus-Derivative+word problem help.

[stanton]

Calculus-Derivative+word problem. help:(

Homework Statement

Two snails are sliming along my square patio's edges. One is on the north edge, 120cm away from the northeast corner and traveling directly east at the snail's pace of 6cm/min.
The other is on the east edge, 50cm away from the northeast corner and traveling north at 4cm/min.
At what rate is the distance between the snails changing?

Homework Equations

I do not know what equation to use. But I used root(a²+b²)=c But I don't think I am using the right equation.

The Attempt at a Solution

let time be t, and upside and right be positive.
snail no.1:f(x, y)=x_i+y_i, x=6t-120, y=0
snail no.2:g(x, y)=x_i+y_i, x=0, y=4t-50
d(distance)=root[(6t-120)²+(-4t+50)²]
= (52t²-1120t+16900)^1/2
So this was the answer I got.


But I am now learning derivative and increasing and decreasing function. So I don't think this should be solved this way. There must be something related to derivative when solving this problem. My prof must have gave us this problem in order to let us solve with the method which we are learning, isn't it?
And I also think the answer is wrong. What should I do? How do I solve this prob?
And if I solved in right way, should I take the derivative of my answer to be the real answer of my problem?

 

[Dick]

I think you solving it in exactly the correct way. Except I get (6*t-120)^2+(-4*t+50)^2=52t^2-1840*t+16900. Now just take the derivative with respect to t and put t=0.

 

[stanton]

Thank you so much!
So I did this way.
=1/2(52t^2-1840+16900)^-1/2
=1/2root(52t^2-1840t+16900)
I took the derivative of my answer. and I put t as zero:
1/2root16900=1/260! (this is not factorial.. I am just excited!)
I got the final answer. This is the exact answer to my snail problem, right?

 

[Dick]

Aren't you forgetting to use the chain rule? Where's the derivative of 52t^2-1840t+16900? The snails are approaching each other, right? Shouldn't the derivative be negative?

 

[stanton]

Okey. Thank you again. I almost forgot that. :)
Chain rule: (u') x (nu^n-1)
(52t^2-1840t+16900)^1/2
1/2(52t^2-1840+16900)^-1/2 x 52t-1840
So, -1840/260=-11.5

 

[Dick]

Yeah, you are doing very right. Except you are being really sloppy. Maybe you are being too excited. -1840/260 isn't equal to -11.5, at all.

 

[stanton]

Oh, My! I AM really being sloppy... I am so sorry. The answer is -7.08.
I must be careful next time...
I really appreciate for your help. Sorry to bother you frequently with those foolish mistakes like forgetting chain rule and -11.5. Thank you so much!