I'm no pro but I've done lots of painting for myself. You can't do the job you describe quickly. It takes time to have it turn out right. I would start with the ceiling using a roller. I personally apply paint slowly with a roller. Otherwise specks of paint will go everywhere. Most people I've seen like to slap it on. I don't think you'll see too many pros do that especially with a ceiling. After the rolling use a brush to get the edges of the ceiling where the roller could not cover. You don't care about getting some white ceiling paint on the walls because you will be coming back with whatever the wall cover is later. When finished with the ceiling the ceiling white should be extending down a couple inches on all the walls.
Now start rolling on the wall application. You don't care if the ceiling is dry yet because the ceiling will continue to dry as you apply paint to the walls. Did I mention an open window to assist drying? Resist the temptation to get the roller close to the ceiling. You just did a great job on the ceiling. Don't mess it up by getting too close with the wall application. Again, take your time with the roller. You're watching for the right amount of paint on the roller at all times. Too much or too little paint on the roller will not give the best results on the wall.
After taking a break, you're gonna need one at this point, start cutting in the top of the walls. The key is the right amount of paint on the brush. And of course a good brush. I load up the brush and then dump about half the brush's load somewhere near the top of the wall. Now that I have a managable amount of paint on the brush I hold it near where I want my line, press the brush down a little to spread the bristles and then draw the line that I want. I then pat the brush where I left the excess paint and do the above process until I've used all of the first brush load of paint. Drawing the line gets easy after you've done it on a bunch of jobs. However, it does take a while to develop the skill. I cut in windows, doors and baseboard in a similar fashion.
Now for the time thing. I don't see how a good job could possible be done in less than four hours. It would probably take me six. 15 x 15 is big and there is the setting up of drop cloths, moving the ladder over and over, moving the cans etc. around the room and all that time consuming cutting in, not to mention the cleanup. And don't forget breaks and lunch. You can't work without fuel.
The key thing is to give yourself enough time to do the job right. If you're weak on cutting in this could easily be an all day job.