I would keep figure. I heard it before, hence it doesn't sound wrong to me, but it's colloquial. If you figured it out, I'd wonder, "out of what? What is it?"
"I didn't take (a) long (time) to"
Why the indirection? What is It? The figuring, certainly, but I don't think you should use a personal pronoun to denote an infinitive verb. Not saying the passive was entirely wrong, but I'm unsure how to transform it. Something along the way of "It didn't take a lot of my time"
"my friends darted to class, leaving me there, thinking what to do next."
That sentence is much more troublesome for me. What's with all the commas? It potentially means the friends where leaving while thinking. I am not sure, though.
For basic English, a teacher would probably emphasize to use a more formal style, e.g. understand or hypothesize instead of figure. Do you just say figure because you picked it up as a synonym for another word?
Going out on a limp i'd guess, it's somehow connected to idea, which in old greek might mean form, while figure also means form, so you are basically saying you idead? Whereas the meaning of figure out is closer to envision, i guess, like produce a figure out of material. Or maybe figure is related to numerals, so to speak as you calculated your chances, you counted your options. Anyway, the link in the other answer gives imagine, which is more or less suitable.