I do not believe there is a simple way to do this. Maybe there is a third party statistics website that could help you, though the ones I know of do not have that particular statistic.
The best suggestion I have for you is to put them all in a playlist, and YouTube will tell you how long all of the videos are together. I'd suggest temporarily clearing your Watch Later playlist, maybe making a copy first, and hit the watch later button on all of the thumbnails of the videos. Of course, do this in a logical manner; sort the videos by date uploaded or something. Once you have them all in a playlist, you can simply go to your list of playlists and read the time. Hope that works for you. I could not think of anything better...