Kenkoooo's AtCoder problem recommendation has columns for solve probability and median solve time. I understand that solve probability is computed using the user's internal Elo, but how does kenkoooo estimate median solve time? 
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You can try to read the source code: github.com/kenkoooo/AtCoderProblems
In particular, the solve time is computed here in atcoder-problems-frontend/src/utils/ProblemModelUtil.ts, which seems like a linear function of your rating times
problemModel.slopeplusproblemModel.intercept. These two parameters are computed from a simple linear regression on participants' ratings and their solve time of the problem, not particularly sure about this but you can take a look at the time-estimator folder and function.py.