The Massachusetts Bay Transportation Authority will push back final trips on all subway lines and the Mattapan Trolley by roughly one hour on Friday and Saturday nights beginning 24 Aug., the agency said Tuesday. Service will also run later on eight frequent bus routes those evenings, while five of the system’s busiest lines—Routes 23, 28, 57, 111 and 116—will operate on the longer schedule every day. Light-rail and trunk subway segments are slated to maintain 15-minute headways during the added hour; branch and bus services will run about every 30 minutes. To spur ridership, the MBTA will waive fares on all modes after 9 p.m. for five consecutive Friday-Saturday weekends from 29 Aug. through 4 Oct. General Manager Phillip Eng, flanked by Governor’s office officials, said the move responds to input from more than 20,000 riders and mirrors a 2014-16 pilot that ended for budget reasons. Boston’s transit build-out continued elsewhere Tuesday as Mayor Michelle Wu cut the ribbon on a new commuter-ferry stop at Pier 10 in Raymond L. Marine Park, providing direct links to Fan Pier and North Station. The ferry expansion, together with the late-night rail and bus extensions, marks the city’s most significant service increase for night-time travelers in nearly a decade.