@fleetfingers: Thanks for the advice. It was quite helpful.
@ongaku: I don't tend to think of myself that way in general. I mostly only think of that when regretting wasted time, but thabk you for the advice. I'll try to make sure I don't think too highly of myself.
@pianisten:
I usually start out by playing scales, something I recently started doing again after a couple years af neglect (my decision, one that made my teacher happy). Then I'll play through the piece I'm working on and think about what sections need the most work. I'll then go to those sections and practice them slowly and repeatedly, half the time with and half without a metronome. I'll then play through the piece again to see if I've really mastered the changes I've made. If not, I'll go back. If so, I'll do the same with other sections. I'll then play scales again and move on to another piece. Along with the Rhapsody, I'm playing a Mozart duet in C major and a Scarlatti sonata in C minor (don't remember the opus/K).
I know I could and should play more tham I do, but 15 hours a week is about 15 times as much as I used to play. Over the summer, I will have more time to play more. I'll also look into taking lessons from a different teacher for a while.
More about myself: I'm 17 and have played piano for around 10 years. After 6 years, my parents gave me the option to quit (I was required to play before that) but I agreed not to quit if my parents would stop bothering me by telling me to practice (although they were never exacrly taskmasters) as long as I practiced at least 20 minutes a day 3 times a week. The intention was for me to practice much more than that, but I didn't. This fall, I came back to start lessons again with, for whatever reason, a lot more drive to get better and practice. My teacher saw this and gave me a Brahms piece that was much more difficult than anything I had played before. After learning that, I read through the 1st Rhapsody a couple times and liked it, so I asked my teacher to let me play it. He warned me it was difficult but agreed when I said I would make sure to put enough time into it. I have been working on it for a couple of weeks so far and have most of the notes down. And that's about it.