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\section{Introduction}
Galaxies in denser environments are more likely to have suppressed (quiescent)
star-formation rates (SFR) star formation and little-to-no cold gas than galaxies of similar stellar mass, $\mstar$, in less dense environments.
The observed environmental effects in the Local Group (LG), specifically on the satellite dwarf galaxies within the halos of the Milky Way (MW) and Andromeda (M31), are particularly strong
\citep[e.g.,][]{Einasto1974,Mateo1998,McConnachie2012,Phillips2014,SlaterBell2014,Spekkens2014}, \citep[e.g.,][]{Einasto1974,Mateo1998,GrcevichPutman2009,McConnachie2012,Phillips2014,SlaterBell2014,Spekkens2014}, even compared to the effects on (more massive) satellites within massive groups/clusters.
Specifically, the dwarfs around the MW/M31 show a strikingly sharp and nearly complete transition in their properties within $\approx 300 \kpc$ (approximately the virial radius, $\rvir$, of the MW or M31), transitioning from (1) having irregular to
elliptical/spheroidal spheroidal morphologies, (2) having most of their baryonic mass in cold
atomic/molecular atomic gas to having little-to-no measured cold gas, and (3) being actively star-forming to
quiescent \citep[e.g.,][and references therein]{McConnachie2012}. quiescent.
This trend has just a few exceptions:
four 4 gas-rich, star-forming galaxies persist within the halos of the MW (the LMC and SMC) and M31 (LGS 3 and IC 10), and 3 - 4 quiescent, gas-poor galaxies reside
just beyond $\rvir$ of the MW (Cetus and Tucana) and M31 (KKR 25 and possibly Andromeda XVIII), though Cetus and Tucana likely orbited within the MW halo \citep{Teyssier2012}.
This efficient satellite quenching is particularly striking because, other than KKR 25, at $\mstar<10^9\msun$
all \emph{all} known galaxies that are
sufficiently isolated
(beyond $1500\kpc$ of ($>1500\kpc$ from a more massive galaxy) are star-forming \citep{Geha2012, Phillips2014}.
Thus, the MW and M31 halos exert the strongest environmental influence on their satellites of any known systems, so the LG is
perhaps the most compelling laboratory for studying environmental processes on galaxies.
Several environmental processes within a host halo regulate the gas content, star formation, morphology, and eventual tidal disruption of satellite galaxies, including gravitational tidal forces \citep[e.g.,][]{Dekel2003}, galaxy-galaxy interactions \citep[e.g.,][]{FaroukiShapiro1981} and mergers \citep[e.g.,][]{Deason2014a}, tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001,DOnghia2010}, ram-pressure stripping of extended gas around the satellite \citep[e.g.,][]{Larson1980,McCarthy2008} of the cold inter-stellar medium \citep[e.g.,][]{GunnGott1972,Tonnesen2009}, many of which can be assisted by feedback from stars and/or AGN within the satellites \citep[e.g.,][]{BaheMcCarthy2015}.
One strong constraint on
the their relative effects
of these processes comes in determining the
dependence of the timescale of environmental
quenching quenching, including its dependence on
both the mass of
both the
host satellites and the
satellites, host, as
has been done in previous works
have explored at higher satellite
mas scales masses \citep[e.g.,][]{Balogh2000,Wetzel2013,Hirschmann2014,Wheeler2014}.
While 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
quenching quench star formation
as a function of satellite mass. in satellites in the LG.
In this letter, we combine the observed quiescent fractions
of for satellites in the LG with
the typical virial-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 LG.
Motivated by the results of \citet{Wetzel2015}, we also consider the possible impact of group preprocessing on satellites before
falling they fell into the MW/M31 halo.
