Remember that distance = rate times time.
First distance = 168 miles; time was 3.5 hours. Rate was 48 mph.
5 miles per hour faster than that was 53 mph.
Second distance = (2 1/4 hours)*(53 mph) = 119.25 miles
Total distance driven in those 5 3/4 hours: 168 mi + 119.25 mi = 287.25 mi