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? 
| # | User | Rating |
|---|---|---|
| 1 | Benq | 3676 |
| 2 | Kevin114514 | 3659 |
| 3 | jiangly | 3640 |
| 4 | turmax | 3450 |
| 5 | tourist | 3382 |
| 6 | strapple | 3360 |
| 7 | Um_nik | 3354 |
| 8 | squareOf105 | 3348 |
| 9 | maroonrk | 3312 |
| 10 | idontwannadothis…e | 3191 |
| # | User | Contrib. |
|---|---|---|
| 1 | Qingyu | 156 |
| 2 | nik_exists | 151 |
| 3 | maspy | 149 |
| 4 | AmShZ | 145 |
| 5 | Um_nik | 143 |
| 6 | Errichto | 139 |
| 7 | BledDest | 136 |
| 8 | adamant | 135 |
| 9 | maroonrk | 132 |
| 10 | cry | 130 |
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.