Boat Odds When flop Trips

[wacki]

If you make trips on the flop, and there is a 3 flush on board, then:

You have 6 out's for boat, and 1 for quads making (6+1)=7 outs for turn[7/46 = ~15%]. If the Turn is blank then you will have 9+1 outs for the river[10/45 = ~22.2%].

For the turn and river its
1-(40/47)*(36/46) =~33.4% making a boat

Is this correct? The math looks ok to me, I just didn't think the odds of making a boat/Quads when you flop trips were that good.