THANE: What, there are more problems?
COLE: You didn't flip the sheet over.
THANE: OK. "A riverboat on the Mississippi River travels 30 miles upstream in 2 hours and 30 minutes. The return trip downstream takes only 2 hours. Part a: find the rate of the current. b: Find the rate of the riverboat in still water." OK --- you've just written down the answer. I have no idea if it's correct. It's got to be wrong. So, erase that and start of by letting c equal the rate of the current, and s = the rate of the riverboat. Then you'll have two equations, one upstream, and one downstream...
COLE: I don't need the variables. It's 30/2.5 or 12 miles per hour one way, and 30/2 = 15 the other. So take 3 and divide by two, that's the current, 1.5.
THANE: What? You could be right. Hold on. Oh, you're saying 3 because 15-12 is three?
COLE: Right.
THANE: OK, I guess that is right. But, such insights are not helping you in this wretched subject, 8th grade algebra. You messed up the Anita and Tionna problem because you didn't define the variables, you had an equation wrong when you did it in your head. What I'm saying is that 8th grade Algebra is a pernicious, boring subject and you'll keep making mistakes unless you plod through the problems in the formulaic way I recommend. Even on the riverboat problem, look, you wrote the speed of the current, but you didn't answer the other part, the speed of the riverboat.
COLE: 13.5. I got the right answer.
THANE: But you didn't write it down. So, think about the grader: you'll get 1/2 credit, even though you know how to do it, and in fact have even dodged the whole point of posing the problem. So, on this problem, yes, nice insight OK, but on the ratio of girls to boys problem...
COLE: I got it right, check it.
THANE: [pause] OK, you got it right. But, you missed the trains travelling problem, again because you scrawled stuff and got messed up. You didn't check. I'm supposed to be good at math, right? Everyone says that. But I know I make many many, many, mistakes; I expect to make mistakes, and I find them. Then I kill them. But I check to make sure the mistake is dead. Math is a subject like that --- you have to check and recheck that the vampire is dead. Then you stick another stake in him, just to be sure. You are not an algebra God, and you are making mistakes. That's why you're a borderline A student, rather than coasting. You seem to think Algebra is a subject that can be treated via a few messy scribbles, some reasonable, or even inspired, guesses and an answer that you don't even bother to check: I'm saying you're wrong.
COLE: I don't need the variables.
THANE: Argh, you need the variables!
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