Back in my school days I was taught that a person could live for three to four weeks without food but with water. The knowledge is still applicable, but there are other factors that dictates the surviving period.
Mental strength, health condition, body weight, climates etc. could play their part in determining the survival length. Under ideal circumstances a person could live without food for six to eight weeks, or even longer in extreme cases.
Not sure if there’s any official record for the longest survival without food. The longest I managed to find is 73 days during the Irish hunger strike in 1981 [wiki]. The strike was called off after ten prisoners had starved themselves to death.
Kieran Doherty died after 73 days. While Laurence McKeown survived for 70 days after his family authorised medical intervention to save his life.
[Update] Terence MacSwiney, also an Irish, died after 74 days in a hunger strike in 1920. He might have received medical attention in his last days though.