Final answer:
The author's description of Petra as "a city half as old as Time" represents a hyperbole, an exaggerated statement meant to emphasize the ancient city's age and grandeur.
Step-by-step explanation:
The author who describes Petra as "a city half as old as Time" uses the figure of speech known as a hyperbole. A hyperbole is an exaggerated statement or claim not meant to be taken literally. It is used for emphasis or as a rhetorical device to convey strong feelings or create a strong impression, but is not intended to be taken literally. The phrase "a city half as old as Time" exaggerates the age of Petra to emphasize its ancient history and the grandeur that comes with it.