A group of friends went on a road trip. They drove for 3 1/2 hours at an average speed of 60 miles per hour. Then they stopped for a break and continued driving for another 2 3/4 hours at an average speed of 45 miles per hour. What was the total distance they traveled during the entire road trip?
The total distance traveled during the first leg of the trip is 3 1/2 hours x 60 miles per hour = <<3.5*60=210>>210 miles.
The total distance traveled during the second leg is 2 3/4 hours x 45 miles per hour = <<2.75*45=123.75>>123.75 miles.
Therefore, the total distance they traveled during the entire road trip was 210 + 123.75 = <<210+123.75=333.75>>333.75 miles. Answer: \boxed{333.75}.