How much time has passed before the nurse could tell Penelope that Telemachus had left for Pylos?

The nurse could tell Penelope that Telemachus had left for Pylos after a significant amount of time had passed since his departure. Specifically, it was around the time when Telemachus had already begun his journey and was far enough along that news of his departure reached her. This suggests that it took several days for Penelope to learn of his absence, emphasizing the communication gaps of the time.