Calculate a speed of colour-shifting

Look at Reply #2 for an easier explanation!

public Background(Color cc, int aa, int tt) {
		c = cc;
		s = ???;
	}

cc is colour, aa is colour deviation and tt is time in seconds. The game updates 60 times/second.

For example, if I passed in Color.PINK, 50, 3 I would basically say this:
My background is in the colour pink by default.
Its colour is going to continuously shift shades.
The time for a shift from the darkest shade to the brightest is going to take 3 seconds.

How would I calculate the speed s with known deviation and time?