Reading about missions that have made or will make heavy use of gravity assist (Galileo, Cassini, MESSENGER, BepiColombo...) made me wonder about what if a heavy unmanned ship (BFS?), with all the necessary fuel to do orbital insertion and landing on Callisto or Mercury (for the purpose of establishing a base, perhaps using the same approach as SpaceX plans to do on Mars), follows a similar trajectory to them, and at the appropriate time a much smaller manned capsule docks with it (that is; at the last earth flyby for a Jovian-bound ship / a quick Mariner-10-like trajectory to dock with the mother ship after its last mercury flyby).
This would make the manned part of the journey considerably shorter, perhaps 2 years rather than the 6 required in the case of Jupiter, and a number of months rather than over 7 years for Mercury. The big ship would be relied for all the fuel-consuming tasks of matching velocity with the target, orbital insertion, and landing.
Now, it seems clear that this totally depends on whether the velocities and trajectories of both vehicles can be matched. I don't seem to be able to find the relative velocities at which Galileo passed Earth in 1992, Cassini in 1999, and Mariner 10 approached Mercury in march 1974. This would help to clarify my question.
This is purely a numbers question, so it's clearly not "too broad" or impossible to answer. Thank you.