Your answer would be that the participial phrase is "talking rapidly" and the word it modifies is the pronoun <em>she.</em>
Explanation:
The participle in the sentence above is "talking rapidly". This participial phrase is a present participial phrase as it ends in -ing. Since all phrases requiere two or more words, participle phrases often include objects and/or modifiers. In this case, the participle phrase contains a modifier, the adverb "rapidly". What is more, participle phrases always function as adjectives by adding description to the sentence. As you can see, the participle phrase in question premodifies the personal pronoun <em>she. </em>