Most people, even those who have never studied the Latin language, recognize and know the meaning of the phrase tempus fugit -- "time flies." Popular culture has included the inseparable addage "when you're having fun" and so it remains.
Very few realize, though, that the original Latin phrase is tempus irreparabile fugit from Vergil's Sed fugit interea, fugit irreparabile tempus, singula dum capti circumvectamur amore (Georgics 3.284-5) and is much closer in meaning to Horace's carpe diem than the popular expression of surprise that the evening has passed while we were eating, drinking, and being merry.
Tempus irreparabile fugit essentially means "irrevocable time flies" or, better, "time flies and it's never coming back again." So... time does fly but not because you are having fun; rather, the reverse is true: you need to have fun because time flies.
The river in the picture is the Rio Grande winding its way through New Mexico. I took this photograph while playing hooky from the 2005 ACL Institute in Albuquerque.