Really depends on how much you will play. If you are the type to play until you beat the game then it will take about a day or 2....if you are more casual like me it will take about a week. I just finished part 2 and i have had the game since last friday but barely played until yesterday.
It took me about 2 days: I played through the first 2 chapters on day 1 and was hooked after that so I marathon'd chapters 3, 4 and 5 on day 2. Episode 4 seemed to be the longest one. In total: about 12 hours.
R.I.P. Dad, you are my hero and I will always love you 4/18/1948 - 10/22/2011