My method of extract brewing:
1) heat ~ 6.5 gal of water in the brew pot with steeping grains in a cheesecloth bag
2) over the course of 20-25 minutes, the water should be in the 130-150 range, turn the heat down
3) get my old, 3 gal brew pot and add about 1 qt of hot steeping liquor. Pour the LME into that to thin and dilute. Add some enough steeping liquor to the LME container to eventually clean it out.
3) - alternative if using DME, do the same thing, but add the DME to a big bowl and whisk to break up clumps
4) The kettle temp is probably around 160-170 by now, remove those grains and add the diluted extract to the brew kettle. Might have to rinse out the mixing bucket.
5) rinse the grains with some water and add that goodness to the kettle.
All the above should take less than an hour.
My record extract brew with that sort of process, including clean up is 2hrs 45 min
My record ag brew with batch sparging is about 4 hrs - not bad at all (thanks Denny!)