Agatha Christie's Miss Marple: 4:50 from Paddington (1987)

When Miss Marple's visiting friend sees a woman being strangled on a passing train, they immediately report it to the police. Inspector Slack sees Miss Marple as a bit of a busy body and drops the investigation after only a few days. Miss Marple however determines that there is only one spot along the line where a body could have been dumped and it happens to be very near the Crackenthorpe estate. She asks a professional housekeeper, Lucy Eyelesbarrow, to go there undercover as a domestic. She soon finds the dead woman's body at which time the police take on a renewed interest but it is left to Miss Marple to solve the mystery.