Good attitude - nothing good happens fast in this hobby. There is no firm rule about how long a tank takes to cycle. It may take no time at all, or may take 6 weeks. With the live rock and sand you ahve I would guess that cycling shouldn't take a long time, but you don't go by time, but by water parameters. Put a piece of cocktail shrimp in the tank and measure the ammonium concentration daily until it reaches 1.0, then remove the shrimp. Monitor ammonium until the levels drop to zero, then measure nitrite levels - when they fall to zero you are ready to go. If the live rock is loaded with bacteria this could occur immediately and the ammonium levels might not rise to 1.0 at all (this is called a soft cycle). Good luck - keep asking questions and stay patient.
