Whenever I read about the (motorized) washing machine, there is always a comparison to women doing their laundry at home, and often a mention of the washboard.
I know steam laundries existed in cities (as small as a couple thousand, at least) as far back as the late 19th century, at least. I can understand that rural people wouldn't really be able to use them.
I have seen prices of $.05 or $.06 per pound for rough dry in the first decade of the 20th century in the US, but I don't really know how much that was for most people.
And when they were used, would it be for all washing or just for linens and such?
I guess I'm interested in what percentage of urban women (though I know the world has increasingly urbanized, as a rule) went directly to a washing machine from hand-washing her own family's laundry v. how many used some sort of service prior. And how the costs compared.
I wrote an article on this (in a previous century)!
Working with two of my student interns, we did an analysis of laundry work in Virginia City, Nevada. By the early 1860s, there was a large steam laundry that did most of the commercial work - processing linens and other things for hotels, etc. Neighborhood laundries did most of the private work. These were generally operated by small groups of young Chinese men or single Irish women who were typically widowed or no longer living with husbands. Irish women served the Irish-American community, which paid for the higher prices in order to subsidizing these women. Others tended to patronize the Chinese American establishments - although there was made difficult by racist propaganda about unsafe conditions in Chinese laundries.
Other women often provided services for lodgers/boarders, but doing laundry work for anyone outside the household was something most women gave up on because it was terribly hard work and the pay was low (unless they were members of the Irish community).
I have not seen any primary source information on your specific question about the transition from hand washing to a washing machine, but from what I gather, most household did just that. The house where I live, which dates to 1875, has all sorts of handwashing equipment in the basement. I'm sure everyone was glad when they acquired their first washing machine.