Final answer:
The quote demonstrates situational irony, where the man's statement about the lack of time is contradicted by his own action which indicates that time is not as pressing as he asserted.
Step-by-step explanation:
The type of irony used in this quote is situational irony. Situational irony occurs when there is a contrast between what is expected to happen and what actually occurs. In this case, Jonas expresses his interest in hearing the story of the man's life, and the man's response is unexpected. Instead of welcoming Jonas's interest and expressing a willingness to share his life story, the man waves his hand impatiently and says there's no time, creating a situation contrary to what Jonas, and possibly the reader, might have anticipated. This creates a subtle but effective form of situational irony in the interaction.