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1. To bind, fasten, or secure something with or as with string, cords, rope, etc. In this usage, a noun or pronoun can be used between "tie" and "up." Make sure you tie up the boats at the dock so they don't get swept down the river. Will you tie these bundles of paper up for me, please?
2. To keep someone busy, occupied, or engaged. In this usage, a name, noun, or pronoun can be used between "tie" and "up." The meeting tied us up for most of the afternoon. I just have a couple of questions, so I won't tie you up for too long.
3. To block, impede, or delay something. In this usage, a noun or pronoun can be used between "tie" and "up." The construction has been tying up traffic on Main Street for nearly a year now. They've tied our application up in court, so we haven't made any real progress lately.
4. To commit something to a prior use, thus making it unavailable for anything else. In this usage, a noun or pronoun can be used between "tie" and "up." I wish I hadn't tied our savings up in that bogus real estate scheme. We've tied up too many of our resources in this project already.
5. In a competition or contest, to achieve a score equal to one's opponent. That amazing touch down has tied the game up as we go into half time. One more correct answer and you'll be able to tie things up.
Fig. busy. How long will you be tied up? I will be tied up in a meeting for an hour.
mod. busy. I was tied up and couldn’t get to the phone.