The round-trip time (RTT), defined as the time elapsed for transmission of a data packet to travel from one endpoint to the other and back again, is an important parameter for Internet quality. This paper proposes an extended version of the well-known SYN/ACK (SA) methodology for passively measuring the RTTs over Transmission Control Protocol (TCP) connections. Differently from the original version of the SA methodology and the rest of studies in the related literature, the proposed passive methodology measures not only the total RTT of an end-to-end connection but also the proportion of the existing connection sections on this entire RTT in a passive way if the connection between client and server is established via intermediate stations. A distributed measurement architecture has been designed that implements the extended SA methodology. Through tests in a controlled laboratory environment, various verification and performance evaluation experiments were conducted to determine the accuracy level of the measurement technique and how the distributed architecture behaves regarding resource requirements as the amount of incoming network traffic increases. Accuracy verification experiments show that on average about 92.66% of the passive measurements are within 10% or 5 ms, whichever is larger, of the RTT that ping would actively measure. Furthermore, the results reveal that using today's commodity hardware, the designed distributed architecture exhibits acceptable satisfactory scaling performance and can practically be used to passively measure RTTs of each hop within medium-sized communication networks.