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Some people, whose name will go unmentioned (but their initials are Mightyqueen801), do not actually know what algebra actually is.
Ignorance is bliss. She's happy. Leave her be.
The half of each time-frame thing is obvious. I'm not sure I would have figured out to split the 5 minute difference between them and used the 2-1/2 to bring them both to the same number.
LOL, WHAT? I don't know if they are the answers or not! I can't do algebra, remember?
I came up with 17-1/2 minutes because if he normally cleans in 30 minutes, and she normally cleans in 40 minutes, that means with two of them working, half the time for him would be 15 minutes and half the time for her would be 20 minutes, so I took the extra 5 minutes difference and cut them in half and added those 2-1/2 minutes to the 15. Or subtracted them from the 20, take your pick. That's the best I could do in my head on the train, but that was my logic.
With the tank thing, it takes 50 minutes to drain the tank but you are also filling it which takes 60. By the time the tank is drained of the original whatever is in it, it has ten minutes left of the new whatever to fill it. Then it takes another 50 minutes to drain it again. But then it has drained ten more minutes, so maybe that's wrong. Maybe it's 100 minutes, not 110.
Anyway, NONE of that is algebra!
Oh, you are very good at explaining things. I now understand how to do the first problem. That even makes sense way out here on Mars.
What about the ground beef problem? I can see how someone might have to figure that out but it is totally 100% beyond me. I don't even have the slightest clue. And it makes me feel like CRYING AGAIN.
You can understand it if it's presented in a way that "connects" with you. It's a matter of finding that instructor/technique. It may take a long time, but it will come if it's presented to you properly (for you). Check the college's developmental math specialists or those who work with math anxiety.
I have taught remedial math in a local university for 20 years now. Of course it takes study and time, but study and time will do nothing for you (and actually hurt you) if you are not thinking about this stuff (algebra) properly. It often tends to be an actual modification of the way the algebra is perceived that helps more than any amount of grinding study or time. The time factor is important (and let's face it, math takes time to get down for everyone), but is counterproductive until that perception of the algebra is flowing properly through your brain.
Think of it as something like learning classical guitar--it doesn't matter if you are practicing 10 hours a day if your basic posture, hand position, finger angle/attack is wrong. In fact, it's devastating because your "muscle memory" has to be undone and you have to start all over with proper technique before you can actually learn the music so that it works and sounds good. Same with algebra--if you are actually working on the problems themselves before your brain is correctly approaching the subject, you're simply reinforcing bad thought processes that result in an inability to "play the music" (of math).
That's what's missing in algebra: Logic. You're just supposed to accept on faith that X=something but what if it doesn't? Who says it does? X is a letter of the alphabet. Now geometry is logic, it is simple and straightforward. Besides that, you can picture it. Algebra expects you to take too much of a leap into the unknown, a leap of faith off a cliff.
I still think they should have different class lengths for different lengths of students when it comes to Algebra and beyond.
This whole thing of memorizing many different formulas within the time-span of 3-4 months just doesn't bode well with myself and others that lag behind the academic drag-racers.
If you can hack it within that short of a time frame, then good for you.
I'm quite sure it will get you all the financial assistance you'll need.
The rest of us have to work and do this on the side due to the way our brains grasp certain subjects.
Deep down, some of us desire to make ourselves look/at better in some way.
We just don't want to repeatedly trip and fall back down the stairs we're trying to climb.
Think of X as a big question mark. Because (in context of an equation) that's what it is. It's simply asking the question, "What does this question mark have to be to make this true?"
Of course, that can be quite complicated or even impossible to answer, but in it's simplest form it's like, X + 5 = 15 or ? + 5 = 15 (so, what number plus five equals fifteen?) And it just goes on and on step by step from there... But THAT's where your "algebra brain" has to start to be able to understand and work the complicated problems.
That's what's missing in algebra: Logic. You're just supposed to accept on faith that X=something but what if it doesn't? Who says it does? X is a letter of the alphabet. Now geometry is logic, it is simple and straightforward. Besides that, you can picture it. Algebra expects you to take too much of a leap into the unknown, a leap of faith off a cliff.
(I wish double quote worked for me--maybe it's something to do with my math disability...)
But geometry is like 1>>2>>>3 and it's true because you prove it as you go along. Also it's true because you can see it or at least visualize it. With algebra you can't see it and there are alphabet letters and equal signs that don't mean anything. You are in a fog.
I was just looking up spatial temporal reasoning--but nothing I can find seems to make sense to me. It says it's what math uses and what geometry uses----but to me, geometry is simple words and pictures and just proving as you go. Algebra is ? At least the hamburg in the grocery store made some sense because it wasn't just a nonsense question made of alphabet letters. It was real. Yet I haven't the faintest idea of how to figure it.
I need clues--like geometry gives you. Geometry comes right out and TELLS you that the diameter of a circle is such and such. It gives you something to start from and you use whatever other clues they give you to prove the answer.
The articles I read also talked about analytical language reasoning. That sounds like what geometry would be but that's not what they said.
For some reason I KNOW that music and math are related but I don't know how and I don't know how I know that. Maybe the beats and the timing and the math of the whole notes and the dotted half notes.....but it's more than that. I'm not that good at music either--but I can DRAW. I'm good at language too but I cannot grasp algebra.
Oh, you are very good at explaining things. I now understand how to do the first problem. That even makes sense way out here on Mars.
What about the ground beef problem? I can see how someone might have to figure that out but it is totally 100% beyond me. I don't even have the slightest clue. And it makes me feel like CRYING AGAIN.
Here's a hint to to solve the groundbeef problem:
Cost of groundbeef A + Cost of groundbeef B = Cost of entire hunk of beef
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I now understand how to do the first problem. That even makes sense way out here on Mars. 
