How long will this take?
That depends.
Will the spec change after we begin?
Are we depending on supplies or inputs from other people?
Will the budget change?
Is this work that has been done by anyone before?
Is this work that has been done by this team before?
Is finishing it fast more important than doing it well or on budget?
Do you want to participate in the work (see the part about the spec)?
What are the incentives of the people working on the project?
How many different people are involved?
Are all the people, budgets and assets in place already?
Who is choosing the tools?
Pathfinding takes longer than path following. Discussions lead to changes in spec. Dependencies always add time.