What Machka said. Depends on your experience with ultra-distance rides. Depends on how many candles you burned on the first double. Depends on whether you want to maximize performance or whether you're riding purely for fun.

For some measure of comparison, I did 235 miles in 12 hours (total time, including off-bike time) at a race on 5/6, and then did 220 a week later on the tandem with Mrs. Octopus (her first double!) in 14:48 (again, total time). After riding the second double on a Saturday, we went out last night (Thurs. night) and had the legs to honk it up on the tandem with the "A" group at the local club ride. Pulled about half of it. Got a 300K coming up this weekend (which I won't be riding for speed after wrecking myself pretty good last night on that club ride).

Anyway, from what you wrote, I'd say you'd be more than good. Three weeks is a long time. Good luck and have fun!