Jana ran the first 3 ½ miles of a 5-mile race in ½ hour. What was her average rate, in miles per hour, for this first part of the race?

To find the average rate for the 3 ½ miles, we need to divide the total distance (3 ½ miles) by the total time (½ hour).

3 ½ miles / ½ hour = 7 miles/hour.
Her average rate for the first part of the race was 7 miles per hour. Answer: \boxed{7}.