Nancy's father calls her in this game, to ask her to visit the telegraph office, and to talk about the mystery. You can call him at the very start of the game, when you haven't met Emily yet. It's impossible for Nancy to talk to him about the mystery at this point. Does that save time?
Let's see. If you call at the start of the game, there are two breaks in the conversation. First, Nancy can say, "The car ran like a top" or "I thought I'd call you first". It's 4-5 seconds faster to select "I thought I'd call you first", because Dad has a shorter response to that.
With the second break in the conversation, you can choose "not yet" and "I wanted to call you first". Dad has the same response to both. So the only difference between the options is how long it takes Nancy to say them. "Not yet" is shorter, by less than a second.
Overall, if you pick the fastest options, the conversation takes about a minute and twenty four seconds. Maybe faster, if you can click on the phone and put money into the slot very quickly. If you do call him, Nancy will mention this in her opening conversation with Jane. That is, when Jane mentions Nancy's father, Nancy says, "I already talked to him, but thanks for the message." So that's about another three seconds added if you call dad first, bringing the total time to 1:27.
If you let Dad call you and end the conversation as soon as possible, the total time is around 1:24. So it's about three seconds faster to not call Dad. Plus, you save some money!
Well, boo and bullfrogs. If you call Dad first, the conversation is faster. But the time you save is cancelled out by the time spent waiting for the operator to connect the call and the time spent talking to Jane. So