Hi Ken! "Of" is one of those tricky prepositions in English. It can be used to indicate a part of a whole item, such as the back of the chair. It can also be used to talk about a measurement or value. For example, "an increase of 10%." "We ran half of a kilometre." In your example, "of" arriving refers to a time period (15 minutes) within reaching the point of your destination. The sentence means that something is going to happen or is required within 15 minutes of arriving at a particular destination. One example, "all cellular phones must be turned off within 15 minutes of arrival at the airport."