Why does BMG in Lakewood close the Yeshiva in the afternoon of a ta'anis like I witnessed on Asarah Ba'teives? Since when are people so weak that it has become seemingly impossible to learn on a fast day? Shouldn't those who learn Torah all day have to put in at least as much effort as those who work and are able to fast a whole day while working?
closed as off-topic by mevaqesh, Isaac Moses♦, rosends, Scimonster, Gershon Gold Jan 11 '17 at 20:26
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Given that some people fast well and others not so well, by not having an official kollel session in the afternoon, they are giving people the choice - presumably those who can learn, do so. A husband may need to lend a hand at home if his wife isn't feeling so good too. Someone who rests in the afternoon will probably be able to learn more that evening anyway.
In Israel, many religious settings (work, schools, etc.) have half or shortened days on a fast day. If everyone could have the afternoon off on a fast day, that would be the ideal, but, of course, in the regular working world it isn't usually possible. Usually when religious people can make schedules independent of outside demands, they can do so with what is more convenient/ appropriate to religious people in mind. Why shouldn't they?
I can't speak for every yeshivah. But, in my neighborhood, on many fast days, esp. during the summer, a number of the rebbes, roshei yeshivot, etc. are invited to speak at community events and other shiurim.
I can't say whether that's a "fair" way to allocate their resources or not. But, I assume that there are enough non-working people around in the community to warrant having them speak at these places such that the communal needs outweigh keeping these people in the yeshiva the rest of the day for the students.