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The following sentence is from an American movie.

It's been awhile since I've been on a date.

Is there a particular reason why people use "have been" instead of "was" there? It seems that from a grammatical point of view only "was" can work there and yet "have been" is much more common. I know that a present perfect is sometimes possible after since but I don't think it's appropriate in the above sentence.

For instance

It's been awhile since I've been here. (fine)

It's been awhile since I've been sick. (fine if I'm still sick)

but

It's been awhile since I've been on a date. ( what?? the date started some time in the past and has continued into the present; we all know that's not the case but why not just use "was" if the date was in the past)
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It is common in speech but generally frowned upon in careful writing, yes. The exception is as you mention. I personally think speakers use it because they are still thinking (subconsciously) of the ongoing passage of time when they mention the starting point.
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Some people tend to use Present Perfect in such sentences because the verb itself doesn't seem enough for them to clearly specify a point in the past.

It's been a while since I was on a date. - You were on a date? But when exactly?

It's been a while since the last time I was on a date. - more specific

It's been a while since I've been on a date. - Possibly you've been on a date a few times, the last one of which is the one you're talking about.

Just thinking out loud, really. I believe different speakers have different views on this.

PS: Please also note that it's "a while", not "awhile".
Mister MicawberI personally think speakers use it because they are still thinking (subconsciously) of the ongoing passage of time when they mention the starting point
Yes, that crossed my mind too. Thanks