It seems like the most time-consuming part is the drying, so another option for you would be to keep using the washing machine and get a cloth drying rack, like this one. It takes about 10 minutes to hang the clothes, you wait till they are dry and then fold them whenever you have the time, maybe days later. Relative to the coin-operated drying machine you save both time and money, reduce energy consumption, and also have no chances of destroying your clothes with a wrong machine setting (as I have done in the past). Of course if $14 a week are insignificant for you then you are taking the best option, but anyone else in a similar situation not willing to spend that amount should consider this option.