The Age of Information (AoI) quantifies the freshness of status updates in a remote monitoring system. This paper introduces a new technique to calculate the average AoI efficiently using stochastic hybrid systems (SHS) analysis. In this paper, the relative freshness of packets in a queueing system is used to define the discrete states of the SHS Markov chain. We validate the average AoI for M/M/1/1 and M/M/1/2 queuing systems with First Come First Serve (FCFS) queuing discipline using this relative freshness approach. Furthermore, we extend our analysis to dual-queue status update systems. We also validate the known results for the packet-dropping probability and the probability that a packet is informative or successfully delivered.