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One strong constraint on the relative effects of these processes comes in determining the dependence of the timescale of environmental quenching on both the mass of the host and the satellites, as has been done in previous works at higher satellite mas scales \citep[e.g.,][]{Balogh2000,Wetzel2013,Hirschmann2014,Wheeler2014}.  While previous worked examined the relative efficiency of satellite quenching in the LG \citep{Phillips2014,SlaterBell2014}, none have constrained the timescales over which environment acts to remove gas and quenching star formation as a function of satellite mass.  In this letter, we combine the observed quiescent fractions of satellites in the LG withthe  typical virial-infall times of such satellites from simulations cosmological simulations, explored in \citet{Wetzel2015},  to infer the environmental quenching timescales of the current satellite galaxies in the LG. Motivated by the results of \citet{Wetzel2015}, we also consider the possible impact of group preprocessing on satellites before falling into the MW/M31 halo.