It can take up to two months to get rid of a wart with duct tape.
The way you're supposed to use duct tape to get rid of a wart is cover the wart for six days with the duct tape.
Then after the six days remove the duct tape and then soak the wart in water and then take a pumice stone and rub the wart with it.
Then put the duct tape back on the wart and repeat the cycle above with a new piece of duct tape and use of a pumice stone for two months.
A better way to remove a wart is by freezing it off with some wart remover.
The wart then should fall off within a week or two.