Duct tape is alternatively known as duck tape, and strangely enough, the latter appellation came first. No matter what you call it, it's a DIY staple found in virtually every utility drawer. When you use this versatile fix-it-all on carpeting and then take it off, it often leaves behind a residue of sticky latex adhesive and only a solvent will remove it. Spray lubricant, rubbing alcohol and dry cleaning fluid are all candidates, but be sure to test first.
Dried Latex Adhesive
No matter why you use duct tape on the carpet, it's important to pull it off as soon as its purpose has been accomplished. The longer you leave it, the more likely it is that the adhesive will dry out and stick to the carpet. Even if the latex-based adhesive is moist and flexible when you pull off the tape, it won't stay that way for long. You may be able to get some of this dried material off with a brush or scraper, but you're probably going to have to dissolve most of it.
Test the Solvent First
Before using any solvent on your carpet, test it on a small, out-of-way patch in the corner or under a cabinet or, if possible, on a scrap piece. You're most likely to have success with spray lubricant, so test that one first. Allow the solvent to remain on the fabric for at least 30 minutes. If the color runs, downgrade to isopropyl alcohol or dry cleaning fluid -- perchloroethylene -- both of which are safer for the rug colors but less likely to do the job quickly. You may also have some success with latex paint remover or lighter fluid.
Soften and Remove the Adhesive
To begin the job of adhesive removal, spray the affected area with the solvent and allow 15 minutes for it to work. It should dissolve the adhesive and loosen its bond to the fabric so most of it comes off when you scrape with a knife or paint scraper. Repeat the procedure as many times as it takes to get all the glue off. If you have a shag rug, it may help to comb through the pile with a comb or a stiff scrub brush. Protect your hands with rubber gloves while doing this.
Clean the Solvent
Once the residue is gone, a strong odor may remain from the solvent, depending on which one you use. In most cases, this odor will dissipate by itself, but if you want to hurry things along, clean the affected area with your favorite carpet cleaner or a solution of mild soap and water. Moisten a rag and rub the cleaner into the carpet, and then let the fabric dry. A final inspection may reveal small bits of residue deep in the pile, and if so, you should be able to comb these out. If not, repeat the cleaning procedure.