Final answer:
The detail in line (22) refines the idea that the cyclists might be related by dismissing the possibility of them being long-lost brothers due to their age difference and circumstances around one's father's death.
Step-by-step explanation:
The detail in the cyclists' dialogue that refines the idea that they might be related is found in line (22), where one cyclist mentions their respective ages and the fact that his father died before he was born, thus dismissing the possibility that they might be long-lost brothers.
This reveals that they were considering their potential relationship due to similarities that had led to confusion about their individual identities. The dialogue focuses on differentiating themselves, which suggests that the resemblance or connection between them was significant enough to require clarification, further supporting the refining of the idea that they could be related.
The detail in the passage that refines the idea that the cyclists might be related is in sentence (21) which states, 'The other shook his head. Something in his handsome face had already differentiated itself from the amused curiosity on his companion's.'
This detail suggests that the two cyclists have a similarity in their appearance, indicating that they could be related. It implies that they share certain physical traits or family resemblances.