The duct tape can help remove a wart but you also need to use a Pumice Stone to file off the wart as well.
Place the duct tape over the wart and leave it on the wart for 3 to 6 days and then remove the duct tape and use a pumice stone to file the wart gently.
Then apply some new duct tape again to the wart and leave it on again for another six days and then file the wart again and the wart should be gone.
A faster way to get rid of warts though is to soak a cotton ball in Apple Cider Vinegar and apply the Apple Cider Vinegar soaked cotton ball to the wart and if possible tape the cotton ball to the wart and leave it on for a few hours or all day if you wish.
The Apple Cider Vinegar will kill the wart and help the wart fall off.
You can also buy some freeze off wart remover from the store or online if you prefer.