Answer: They do not meet.
Explanation:
The distance between Claudia's house and her cousin Brian's house is 16 miles.
Claudia's speed is 8.5 miles per hour.
Brian's speed is 11 miles per hour.
If the part from their houses and travel for 0.5 hours, we have that the distance traveled by Claudia is equal to her velocity times the time she is biking, this is:
C = 8.5*0.5 = 4.25 miles.
So Claudia moves 4.25 miles towards Brian's house in this time, this means that Brian needs to move 16 miles - 4.25 miles = 11.75 miles.
Now, the distance that Brian moves is equal to his velocity times the time:
B = 11*0.5 = 5.5 miles
This is smaller than 11.75 miles, so they do not meet if they only bike for half an hour.