Wow am I dumb.

Ok, it is late and no time to check this, but what do you think of this:

We know equilateral triangle's area A = (3^0.5)/4 * S^2 where S is length of one side.
Write side of triangle as a function of time, S = S(t). We don't know what the S(t) formula is, but no matter.
So can write area as function of time, A(t) = (3^0.5)/4 * [S(t)]^2

Now, differentiate dA(t)/dt. Using the chain rule, we know
dA(t)/dt = dA(S)/dS * dS(t)/dt
The power rule gives us dA(S)/dS = (3^0.5)/4 * 2 * S(t) = (3^0.5)/2 * S(t)
Since we don't know what the S(t) formula is, we do not know exactly what the dS(t)/dt formula is, but no matter.
The chain rule gives us dA(t)/dt = (3^0.5)/2 * S(t) * dS(t)/dt

We are looking at the instant when A = 16. So
16 = (3^0.5)/4 * [S(t)]^2
[S(t)]^2 = 16 *4 / (3^0.5) = 64 / (3^0.5)
S(t) = 8 / (3^0.25)

And at this instant, dA(t)/dt = 4. So
4 = (3^0.5)/2 * S(t) * dS(t)/dt
Substitute in S(t) = 8 / (3^0.25)
And get 4 = [ (3^0.5)/2 ] * [8 / (3^0.25)] * dS(t)/dt
4 = 4 *(3^0.25) * dS(t)/dt
dS(t)/dt = 1/(3^0.25)

Sorry, I just read your initial post then posted an answer, I didn't see that you'd already solved it. Good job.

What was interesting to me is that we have no idea if the side is growing linearly, logrithmically, etc - the solution is a general one.

Oh, I see others beat me to it also. Never mind . . .

Thanks for the answers though. I have no idea what was going wrong when I was doing it. I might have just been the fractions in the exponents, or forgetting the chain rule. I dunno. But you figured it out and it didn't take you 8 hours I'm guessing.

The fractional exponents are confusing.

Thanks for reminding me why I decided to become an engineering MANAGER.:D

Hah :)

HA AWESOME! Few more to go until the 924th, then 928th, then 944th! Woohoo! Porsche can't keep up with me!

and THAT is why I studied chemistry

What?!? It's interesting, but awful. Entropy and Enthalpy, etc, etc.... Blech!

Something about using numbers as in this problem gives me awful brain cramps. Chemistry, even P-Chem was not as painful for me.

I never learned much chemistry. My vague recollection is that it involved way too much memorization for me. For math and physics, you only have to memorize a few formulas and constants (maybe today's students are permitted to have them all programmed into their calculators for all I know).

The awful thing about physics and engineering, IMO, is that you have to carry over numbers and decimals and units for pages and pages, and at the end you've dropped some decimal place 30 lines ago, or have ended up with an area in cubic meters, and you have to go back and check every all over again.

Much easier to do math. It is usually clear when you have the answer. The theorem is proved, or it isn't.

In my line of work the airplane either flies or it doesn't. Simple.:D

Yeah but you don't find out by trial and error - or do you . . .

if it doesn't fly, I bet there will be a trial!