In the UK (which uses first-past-the-post voting) the results of elections are usually declared the next day. If the UK (or any other country) switched to single transferable vote or instant-runoff voting, how long would it take to announce the result of an election?
It might be worth noting that parts of the UK already use preferential voting systems in local governmental elections, including STV in Scotland and Northern Ireland, and the supplementary vote (a somewhat reduced version of the alternative vote/instant runoff scheme) in mayoral elections and the (heavily ignored) elections for police commissioners. These tend to use an electronic scan (optical character reading) to count the vote, rather than rather than full hand counting, which has sometimes lead to delays in auditing, but the results has generally been announced the same day that counting began.
When a candidate gets a majority in the first round, there is no difference. It is also usually possible to determine that all but the top two candidates did not win, even if it is not possible to immediately determine which of the top two candidates did win in IRV (although it is often possible to make a very good guess about that point based on the similarities and differences of the candidates who remain in the running to those who are eliminated).
When no candidate receives a majority, as in Maine this year where the process was used for the first time, it took three or four extra weeks. But, some of this delay was because the process had to be implemented for the very first time in the history of that system being in place. It would probably be possible to shave a week or two off that time frame if the system were more familiar to election officials from prior use. If electronic voting systems, rather than paper ballots were used, it would have been possible to get the instant runoff result immediately, but that would come with downsides with regard to the degree to which the result could be audited.
This is several weeks shorter than a true runoff election in states like Louisiana and Georgia and California where that is held if no candidate wins a majority.
Of course, races where no one candidate receives a majority aren't all that common, a fair number of close races are delayed for a week or two for a recount because the outcome was very close, WA state results are always delayed for a week or two since ballots can be postmarked on election day and received afterwards, and the cases that result in recounts in FPTP overlap somewhat with races in which no candidate receives a majority. So, the extent to which the process delays the last election result being finally decided is quite a bit shorter. Also, while most constituencies in the U.S. get a result that can be called on election night, a significant minority every year do not because vote counting precedes more quickly in some places than others, so even without significant delays, it almost always takes 2-3 days to get a final result.
U.S. ballots take much longer than U.K. and Canadian ballots to count, in part, because U.S. ballots typically each include dozens of candidates and issues (from districts that do not have the same boundaries), and all of the constituencies in the U.K. and Canada are fairly small (and similar in size) compared to an entire U.S. state, a U.S. Congressional District, or a large U.S. county like Los Angeles (with 10.16 million people), while U.K. and Canadian ballots typically involve only a single candidate race on each ballot. Also, election administration in the U.S. is much more fragmented administratively with many more or less independent bodies handling this task.
The last election for Congress in the 2018 election that was decided, in NC where there was election fraud by Republican operatives in excess of the GOP margin of victory wasn't resolved in time for anyone from that seat to be elected by January 3, 2019 when everyone else was sworn in this year.
Thus, it is also important to distinguish between cases where the determination of which party received a majority of the legislative body are delayed v. cases where the determination of the exact extent to which the leading party or coalition has a majority is at stake. Unless the overall national outcome is almost perfectly 50-50, delays from counting non-majority races won't prevent the public from knowing which party will be in control of a body within 2-3 days.