Final answer:
The westward flight with a strong headwind (Option 2) would take the longest because the airplane would have to battle against the wind, reducing its ground speed and increasing travel time.
Step-by-step explanation:
Based on the information provided regarding the effect of wind on an airplane's total velocity, the flight that would take the longest would be: Option 2: Westward flight with a strong headwind. A headwind is a wind that blows directly against the direction of travel. This means that an airplane flying westward against the prevailing wind would be fighting against the wind, resulting in a total velocity that is lower than its velocity in still air, thus increasing the time required to reach the destination.