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%tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001,DOnghia2010},   The key astrophysical challenge is understanding the relative importance of these processes, including which (if any) dominate, and how they might vary across both satellite and host mass scales.  One strong constraint for understanding their relative effects is in determining the timescale over which environmental quenching occurs, including its dependence on the mass of both the satellites and the host, as previous works have explored at higher masses \citep[e.g.,][]{Balogh2000,Wetzel2013,Hirschmann2014,Wheeler2014}. \citep[e.g.,][]{Balogh2000, Wetzel2013, Hirschmann2014, Wheeler2014}.  However, while some 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 quench star formation in satellites in the LG.  In this letter, we combine the observed quiescent fractions for satellites in the LG with the typical infall times of such satellites from cosmological simulations, as explored in \citet{Wetzel2015}, to infer the environmental quenching timescales of the current satellite galaxies in the MW/M31 halos.