For the last few years I've had a galley style kitchen, hence not a lot of floor to mop. I've always gotten down on my hands and knees with a bucket of water to do my mopping. But recently I've found a quicker way to get my mopping done by eliminating the bucket of water, and I believe my floor gets just as clean.
The idea started with the Swiffer wet mop system. Since I don't like a mop per se, and my floors are small in area, I purchased just the wet cloths that attach to the mop. I found they did a very good job on my floor and no bucket of water was necessary.
Being the frugal person I am, I came up with an equally adequate way to get the job done similarly. I got the idea from Don Aslett. He's the guy that used to be on several HGTV program segments teaching us how to clean our homes. He's a pro and had some good timesaving ideas.
Begin with a clean cloth approximately 10"x15". Wet it and then wring it out. Spread the cloth on a flat surface and with your favorite cleaning spray that does not require rinsing, spray one side, flip, then spray the other. (I use Method all purpose cleaner.)
Now, fold the cloth in half, and then in half again. You will end up with 4 quadrants on both sides of the cloth, resulting in 8 quadrants total. Mentally divide your floor into 4-8 quadrants depending on its size. Assuming you've already vacuumed/swept the floor, begin mopping with the first quadrant of your cloth. When you get to the second mental quadrant of your floor, flip your cloth, and you'll have a clean section of cloth for that quadrant. When you get to the third mental quadrant, reverse the fold of the cloth and you'll have cloth quadrants 3 and 4 all clean and available to continue with your mopping.
When the first 4 quadrants have been "used", open up the cloth, and folding the dirty side in, refold the cloth in half, and then in half again. Repeat as above.
This sounds complicated, but it is really easy...easier to do than explain. And I've found that the floor is just as clean as when I use a bucket of water... but there's no bucket to clean up! In addition the whole process goes quicker because you don't have to keep rinsing your mop cloth.
I've been a homemaker for 38 years, and while I enjoy cleaning to some degree, I'm always for getting it done in the quickest and most efficient way, emphasis on quickest. Give it a try...I think you'll like it.