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"I was at the station and was worried about missing the train." Can the second "was" be omitted? I read that conjunctions can connect only the same type of words or phrases (so "at the station" (prepositional phrase) and "worried" (adjective) cannot be connected?)

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Yes, you can omit "was". There are three alternants:

[1] I was at the station and worried about missing the train.

[2] I was at the station and was worried about missing the train.

[3] I was at the station and I was worried about missing the train.


In a coordinate construction, the coordinates are generally of the same category, but they don't have to be. Function rather than category is the crucial factor.

In [1] the coordinates "at the station" and "worried about missing the train" belong to different categories, a PP and an AdjP respectively. But they both function as complements (locative / predicative) of "was" and hence are acceptable.

In [2] the coordinates are both verb phrases functioning as predicates.

In [3] the coordination consists of two main clauses of equal status.


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lifelong learnerCan the second "was" be omitted?

Yes.