As of April 2014, the user can change the length of Snapchat stories. The time limit is 10 seconds, with the minimum being 1.
As soon as the time is up, the story/image/video will be deleted from the Snapchat server and hidden from the recipient's device.
So the longest the recipient can see the snapchat is 10 seconds.
For more on Snapchat, see the Wikipedia article: http://en.wikipedia.org/wiki/Snapchat
To learn more about Snapchat, and pick up some new tricks, have a look at the video below: