How Fast Are Spaceships In 'The Expanse'?

I take a few scenes from the TV show and do the math on how fast the spacecraft are moving, how long they would take to cover the distances in the solar system with brachistochrone orbits powered by the Epstein drive.

To illustrate a number of things I use the magnificent 'Space Engine' -
http://spaceengine.org/

Yes, this contains lots of spoilers.