The first conversation with Emily in the game goes like this:
Emily: Nancy, hi! Welcome to the Lilac...a lot to me.
Nancy: (Generic nice statement. .3 seconds faster to mention Helen.)
Emily: You and I may not...people I know.
Nancy: (Generic nice statement. .7 seconds faster to say "thank you")
Emily: That's why I'm hoping...you and your dad.
Nancy: (Asks about her dad or what kind of favor)
Emily: Your father has a safe, right?
Nancy: (Asks for more information. 1.6 seconds faster to ask a question.)
Emily: See this jewelry? (Shows it off to Nancy.)
Emily: I was hiding it...lock it up in his safe.
Nancy: (Asks about Jane or the situation in general)
Emily: Strange things have been happening...
(Conversation is interrupted)
There are only two points where the conversation diverges. First, when Nancy can say "My dad?" or "What kind of favor?". If you say, "My dad?", Emily says, "Helen says he's a lawyer.", then she shushes Nancy. If you say, "What kind of favor?", Emily shushes Nancy immediately. That's the faster option, by one second.
Second, Nancy can ask about Jane or the situation in general. If you ask about Jane, Emily says she doesn't want to get Jane involved, then she says "strange things have been happening...". If you ask about the situation in general, Emily talks about the strange things immediately. That's the faster option, by about 4.5 seconds.
So overall, you can save 8.1 seconds by picking the faster conversation options.