Healing time varies by the size and location of the injury and each person's body is different. I always heal faster with neosporin than any other brand or if I just put nothing on. If you have larger injuries or surgical sites, consult your doctor before using.
Healing time always depends on the severity of the cut. For instance, minor cuts generally take about 1-3 days, but a slice on my thumb healed in about 10 days. Neosporin always heals my wounds quicker than I expect. I always carry it with me.