This case is different to bog-standard capacitor-resistor circuits in that one resistor is also in parallel with the capacitor, which I'm unable to handle. How does that affect the charging of the capacitor over time?
At least to me, it seems likely that a tiny bit of redrawing makes the circuit more recognizable:
If we ignore the capacitor for a moment, and look only at the resistors, it's now pretty obvious: a textbook example of a simple voltage divider.
This is a pretty straightforward case using Thévenin's theorem to model the source and resistors as seen from the cap.
With the values given, the circuit will behave as though both the voltage and serial resistance is half as large.