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Medway had no answer to the pace and power of Bedford's backline on Saturday, losing 45-15 in Regional 1 South East.
The hosts, sixth in the table, were 20-15 winners at Priestfields in November but on a first-class artificial pitch with excellent playing conditions were rampant, scoring six tries to Medway's two.
Bedford opened their account from a 10th-minute penalty and led 10-0 after a converted score on 20 minutes. The home side then used their swifter players and scored two unanswered tries out wide to lead 24-0.
An Alfie Orris penalty 10 minutes into the second half opened Medway's account, but another team try, converted by Bedford's fly-half, increased the deficit to 28 points.
There was some history to be made when young debutant Adam Richards-Shaw joined the back row following father Simon Shaw and grandfather Mick Shaw - making it a first tri-generation 1st XV family representation in Medway's 91-year history.
Richards-Shaw immediately made an impact and the visitors touched down through Orris, finishing a good set of hands.
Bedford replied, though, with two more tries and with 15 minutes left Medway trailed 45-8.
A converted try gave the visitors the final say, but the defeat was Medway's 14th of the season ahead of their home game with fellow strugglers Sidcup on Saturday (2.30pm).