posted
Actually, it's entirely possible. All those jumps that Voyager has made probably weren't perfectly on course. Even a derivation of a few degrees can put them pretty far off a direct course over distances of thousands of light-years. Presumably the Equinox made some sort of jumps, too (since they were as far along as Voyager in only a little more time), but they wouldn't have been the same ones. These jumps could easily (and even probably would) keep them far enough away from each other that they wouldn't know about each other.
------------------ Homer: "I can see what's happening. They did it to Jesus, and now they're doing it to me." Marge: "Are you comparing yourself to our lord?!" Homer: "Well, in bowling ability..." -The Simpsons
posted
It was never implicitly said that Voyager was the first ship to get the EMH nor the Intrepid class the first class to get it. It was just said it was a new program that Starfleet was thinking about adding to the rest of the fleet. Meaning, the EMH could have been tested on a few ships and/or classes and that the Equinox just happened to be one of the ships chosen for the test.
And the aliens were not a new source of power. It was just an enhancement of the warp drive.
------------------ 7 alarm clock: "Do not touch me." Dilbert: "Then how do I turn you off?" 7: "Believe me, I am plenty turned off."
posted
I think TSN has got it regarding two separate courses home. Consider: until the astrometrics lab came on line, Voyager wasn't on the most efficient course home. It's very likely that the Equinox's sensors weren't working perfectly and that they were on a general course back to the Alpha quad.
Think about it: the ship is about as far away from the Sol System as you can get (w/i the Milky Way) and they need to set a a course for the Alpha Quad. Chances are it's going to be a general course and, as has been said, even a difference of a few degrees, combined with a 6 month - year head start would amount to a large distance between the two ships until they met.
------------------ "A gathering of Angels appeared above my head. They sang to me this song of hope, and this is what they said..." -Styx