How long did Jo have to wait for the final outcome of her venture in Little Women?

Jo's venture is writing a sensational, melodramatic short story to try to win a $100 prize from a newspaper. It takes her six weeks to find out that she has indeed won the prize.
Jo hears about the contest when she goes with a friend, Miss Crocker, to a lecture on ancient Egypt. She meets a boy there who is enthralled with a melodramatic story he is reading. Jo reads it, learns it was written by a woman, and thinks she could do better. That's when she decides to enter the contest.
It's significant that Jo discovers a woman wrote the story, because this helps encourage her to think she can do the same. Her success with winning the contest (although her father denigrates it, telling her she could do better) encourages her to think she could write a sensationalistic novel and, in general, help support her family with her writing.