Agatha Christie 
The Man in the Brown Suit 

Anne Beddingfeld is on her own and ready for adventures when one comes her way. She sees a man die in a tube station and picks up a piece of paper dropped nearby. The message on the paper leads her to South Africa as she fits more pieces of the puzzle together about the death she witnessed. There is a murder in England the next day, and the murderer attempts to kill her on the ship en route to Cape Town.