Final answer:
In fog, when hearing two prolonged blasts on your starboard quarter, you should maintain course and speed, as the other vessel is responsible for avoiding collision.
Step-by-step explanation:
If you are making headway in fog and hear a fog signal of two prolonged blasts on your starboard quarter, it is indicative of another vessel that is under power and making way. According to the International Regulations for Preventing Collisions at Sea (COLREGs), specifically Rule 35 concerning sound signals in restricted visibility, you should maintain your course and speed. Hearing the sound signal on your starboard indicates that the other vessel is the give-way vessel, meaning it is responsible for taking action to avoid a collision. However, constant vigilance is essential, and you must be ready to take evasive action if necessary to avoid an immediate danger.