Final answer:
The athlete heading east is running at a speed of 10 mph, which is the speed given in the scenario for both athletes.
Step-by-step explanation:
The speed of the athlete heading east in the scenario given is 10 mph. Since the question states that two athletes run in different directions at 10 mph and specifies that one heads east and the other heads south, it is understood that each athlete is running at the stated speed of 10 mph in their respective directions. Therefore, the correct answer is option 1) 10 mph.