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Suggest please, is it possible to use past perfect continuous without explicitly
mentioning a span of time something had been lasting for (#1)? Or the only
possibility here is to use past simple?

1. When Sarah arrived, Paul was already waiting for her. [approved]
2. When Sarah arrived, Paul has already been wating for her. [under question]
3. When Sarah arrived, Paul has already been wating for her for about an hour. [modified #2; presumably correct]

Thanks in advance.

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Victor
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1. When Sarah arrived, Paul was already waiting for her. (FINE)
2. When Sarah arrived, Paul had already been waiting for her.
3. When Sarah arrived, Paul had already been waiting for her for about an hour
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Still don't like the second sentence. It is correct but would suggest that paul had left.

The 1st and 3rd are fine.
Oops, it's my typo (has/had). Thanks Dave. So, the second variant is correct, right? And it's not necessarily required to mention a period of time something has been lasting for to use past perfect continuous?
Dave PhillipsStill don't like the second sentence. It is correct but would suggest that paul had left.

The 1st and 3rd are fine.

Got it. Thanks.

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This is my take:

2. When Sarah arrived, Paul had already been waiting for her.

From a strictly grammatical point of view, "when Sarah arrived" is a verb clause modifying "Paul"; therefore the sentence can be written as " Paul had already been waiting for her when Sarah arrived ". From this sentence, I would take it that Sarah had a chance to see Paul as she arrived.
Otherwise, it would be more sensible to write " Paul had already been waiting for her an hour but left when Sarah arrived"; wouldn't it ? So I think # 2 is a valid sentence.