#1 is the common answer. Grammar books and websites usually list "spend time verb-ing" in their explanation of gerunds. Some grammar books avoid the discussion of gerunds and participles by just refering to verb-ing. Some linguists combine gerunds and participles into "gerund-participle" saying that there is no important difference. #2 The inefficient blogger spent her entire afternoon researching and writing one post. (modify the subject “blogger”) I disagree with the writer's explanation that the phrase "researching and writing one post" modifies the subject blogger. As written, the phrase modifies the verb spent and functions as an adverbial phrase. (How did she spend the afternoon? She spent the afternoon researching and writing one post.) My preference is to analyze this as a gerund phase which is the object of the optional preposition in. The inefficient blogger spent her entire afternoon (IN) researching and writing one post. The inefficient blogger / = noun phrase - subject / spent / = verb / her entire afternoon / = noun phrase - direct object / (in) researching and writing one poast / = prepositional phrase - adverbial phrase modifying "spent" / in / preposition / researching and writing one post / = gerund phrase (gerunds and gerund object) - object of preposition "in"/