Final answer:
The average speed of the bicyclist is 9.75 miles per hour.
Step-by-step explanation:
To find the average speed, you need to divide the total distance traveled by the total time taken. In this case, the bicyclist traveled 6 1/2 miles in 2/3 hours. To divide a fraction, you can multiply by the reciprocal. So, 6 1/2 can be written as 13/2 and 2/3 can be written as 2/3 * 3/3 = 6/9.
Therefore, the average speed is 13/2 / 6/9 = 13/2 * 9/6 = 117/12 = 9.75 miles per hour.