“Listen, I don't want to take up too much of your time.”
You're making a sales call to a potential customer. After introducing yourself, you want to make the customer feel relaxed. You let her know that your sales pitch will be short.
Listen, I don't want to take up too much of your time.
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take up (time)
To "take up" something means to use it. This phrasal verb is most often used with "space" and "time":
It takes up too much space.
Having kids takes up almost all of your free time.
This would not work with something like a tool. "Can I take up your hammer?" would be incorrect, for example.
Listen, (sentence)
When you start off a conversation with "Listen", it seems that you want to get to the main point of the conversation quickly. You use it like this:
Listen, I know that we've had disagreements in the past, but I hope that we can work together on this.
Listen, we don't have much time, so let me explain what happened.
There are also other reasons to start off a conversation with "Listen" as well, such as when you're giving advice or when you're introducing an uncomfortable topic.
I don't want to take up too much of your time.
You can use the phrase "I don't want to take up too much of your time" at the beginning of a conversation, to show that the conversation is going to be short:
Hey, Melanie, I don't want to take up too much of your time, but I need to go over these sales projections with you. Do you have a second?
You can also use this phrase to end a conversation politely, in the same way as the similar phrase "I don't want to take up any more of your time":
Listen, I don't want to take up too much of your time, but it was great talking to you.