The NX-01 Enterprise has left space dock and been gone for awhile. They had to travel 8.2 hours at maximum warp with the engines running at 105%.
T'POL: The freighter's warp trail has terminated.
REED: They may have dropped to impulse.
ARCHER: How long to intercept?
TRAVIS: At our current speed, eight point two hours.
ARCHER: Archer to Engineering. Commander Kelby, respond.
KELBY: Kelby here, sir.
ARCHER [OC]: We could use a little more speed.
KELBY: The injectors are running at a hundred and five percent.
The Klingons board the ship and rewrite the warp subroutines when the Enterprise reaches the site 8.2 hours away at maximum warp. After this point Enterprise is forced to travel above warp five or else the ship will blow up.
TRAVIS [OC]: Bridge to Captain Archer. Pressure's increasing again.
ARCHER: Take us to warp five point two.
TRAVIS: Sir, we can't hold that speed for long.
ARCHER [OC]: We're out of options, Travis. Five point two.
Then conveniently the Columbia which is pretty far away at this point can catch up to the Enterprise.
Enterprise "Divergence" (Part 2):
ARCHER: I've just been talking with Trip. Columbia can rendezvous with us in thirty minutes. He says he can restore the subroutines.
REED: He can't do that from Columbia.
ARCHER: We're going to bring him onboard.
REED: The transporter won't operate at warp, and docking's out of the question.
ARCHER: Trip told me you have experience transferring personnel at warp speed.
REED: In training exercises, yes, and at warp speed one. Every move was rehearsed in simulators for weeks.
ARCHER: We don't have weeks.
REED: We'll have to merge our warp field with Columbia's.
ARCHER: T'Pol's doing the calculations now. At warp five, we'll have to move within fifty metres of each other.
Captain Archer states that the Columbia can catch up to the Enterprise when they have essentially the same specs, and the same maximum speed of 5.0 and are a considerable distance from each other. Since the Enterprise has been traveling at greater than warp 5 speeds, they have the same effective maximum speed, and the Enterprise is ahead of the Columbia how is it possible for the Columbia to catch the Enterprise? (And in less then a half hour no less)
Is it that they simply changed heading and turned around back to earth? Even if that decision was made it didn't happen for awhile, they were more than 8.2 hours away from earth. Also Archer doesn't give the command to alter heading and the Columbia did catch up to the Enterprise from behind.