Answer:
Brian needs to complete the 100 mile bike race in a time of 100 miles / (12.5 mph) = 8 hours.
He has already ridden for a distance of 60 miles, so he has a time of 8 hours * (60 miles / 100 miles) = 4.8 hours to complete the remaining 40 miles.
His average speed for the first 39 miles was 16 mph, so he rode this distance in a time of 39 miles / (16 mph) = 2.44 hours.
His average speed for the next 39 miles was 15 mph, so he rode this distance in a time of 39 miles / (15 mph) = 2.6 hours.
The total time he has spent on the first 60 miles is 2.44 hours + 2.6 hours = 5.04 hours.
If he takes a 1 hour break, he has a total of 4.8 hours - 5.04 hours + 1 hour = 0.76 hours left to ride the last 40 miles.
To complete the race in time, Brian needs to maintain a speed of 40 miles / 0.76 hours = 52.63 mph. Rounded to the nearest integer, this is 53 mph.
