Machshirin, Chapter 2, Mishnah 6. This mishnah continues to deal with a city whose residents are mixed, part Yisrael and part nochrim, and it decides a practical question by following which group forms the majority of the town.
The case: "matza bah yarak nimkar", a person finds vegetables being offered for sale in such a city. The produce was harvested on Shabbos and is now on the market at the close of Shabbos. May a Jew buy it right away?
"Im rov nochrim, lokeiach miyad": where the nochrim make up the bulk of the town, a Jew may go ahead and buy the vegetables as soon as Shabbos is out, since we assume that the harvesting was done to supply the gentile townspeople rather than their Jewish neighbors. "Im rov Yisrael, yamtin kedei sheyavo mimakom karov": where the Jewish residents are the larger group, the buyer has to hold off for the span of time in which such produce could have been carried in from a place close at hand.
The reason for the delay is the rabbinic decree known as kedei sheya'asu. Although a non-Jew is not bound by the laws of Shabbos, when he performs a melachah for the benefit of a Jew, the Chachamim forbade the Jew to derive benefit from it. That prohibition does not simply lapse when Shabbos ends: the Jew must first allow enough time to pass for the work to have been done after Shabbos. Here, since the city is largely Jewish and the vegetables were presumably harvested with the Jewish customers in mind, one waits the time it would take to bring produce from a nearby location.
Half and half
"Mechtzah al mechtzah, yamtin kedei sheyavo mimakom karov." Where the two populations are evenly split, the identical delay applies. Following the principle already established in this chapter, a Jewish presence of that magnitude does not get swallowed up in the nochrim. There is a real possibility that the vegetables were cut on behalf of Yisrael, whether in whole or in part, and therefore the shiur of kedei sheya'asu must be kept.
When there is a person of prominence in the city
"Ve'im yesh bah rashus, lokeiach miyad." If a rashus, a person of importance, resides in the city, one may purchase the produce immediately. This follows the same logic seen with the bathhouse: even where the majority of the residents are Jewish, we may assume that the vegetables were harvested for this prominent figure and his household, and not for the Jewish population, so no waiting period is imposed.
Why only "from a nearby place"
The Rav raises an obvious difficulty. Perhaps this produce was actually brought from a distant field, in which case the true time needed to obtain it would be far longer than the wait our mishnah prescribes. Why then does one wait only the interval required to bring vegetables from somewhere close by?
The resolution flows from the nature of this halachah. The requirement to wait is a takanah of the Chachamim, put in place so that a Jew should not come to hand his Shabbos labor over to a nochri. Once a person must restrain himself for some stretch of time, the lesson has registered: I cannot take this produce the moment Shabbos ends, since work performed by a nochri for my sake is off limits to me, and time must first elapse. The Chachamim consequently saw no need to calibrate the delay to the actual distance the produce had traveled. It is enough that there be a shiur, some conventional length of time in which such vegetables are normally fetched, to fix in a person's mind that he may not send a nochri to bring him these items on Shabbos. Hence the measure given here: kedei sheyavo mimakom karov.