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One strong constraint on their relative effects comes in determining the timescale of environmental quenching, including its dependence on the mass of both the satellites and the host, as previous works have explored at higher satellite masses \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 typicalvirial-infall times \textbf{XXX what other  infall timescales are there? XXX} 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 LG. MW/M31 halos.  Motivated by the results of \citet{Wetzel2015}, we also consider the possible impact of group preprocessing on satellites before they fell into the MW/M31 halo.