Answer
See explanations.
Work Step by Step
Step 1. We can simulate the speed of the marathoner as a continuous function. The average speed can be calculated as $\bar v=26.2/2.2\approx11.9$ mph.
Step 2. The initial and final speeds are zero; to have an average speed of $11.9$mph, the runner should have reached the average speed at least once (using the Mean Value Theorem). Let us assume it was at time $t$
Step 3. Because the average speed $\bar v\gt11$mph, from start to time $t$, the runner should have reached $11$mph at least once.
Step 4. From time $t$ to finish, the runner should have reached $11$mph at least one more time.
Step 5. We conclude that the marathoner was running at exactly $11$mph at least twice.
