jk, but still a challenge.

Background: I wanted to share this challenge (math problem) because it marks an interesting time (just a moment in the big picture) for me in my math journey.
Yesterday, I began an online homework assignment that was due today at 6:15 p.m. It was a section on related rates, which is something I'm fairly comfortable with. I did a few of the problems, but noticed that these problems were bad. I mean bad as in they required so much nasty algebra work and stuff. A few of the problems I was unsure of how to set up. For a few hours, I struggled through 10 related rates problems, getting distracted every few minutes (lol sigh*). I actually watched the whole Bionicle Mask of Light movie during this time. (oops)
Anyway, I got to the last two problems. The second to last problem involved a "trough" and some water, the last problem was about a pulley and two carts. In the past I've seen (and done) problems similar to the last one. It's just a two part related rates problem.
I tried the trough one first (I had to ask thkim1011 for some help) but I got it wrong.
I had been chatting with thkim1011 and now I told him about these problems. He asked to see the pulley one, but I wanted that one (greedy me) and I gave him the trough.
A few minutes later: I get the pulley one done, but the trough is a stupid shape (excuse) so I asked kim to help me. We did all sorts of weird things, but we never got the right answer, so we gave up.

About half an hour ago I tried the problem again, and I figured it out.

Here's the problem:
Have fun! (Special awards and commendations to people who solve it)

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