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Similarly, the green curves in Figure~\ref{fig:quench_times} show the quenching timescales for more massive satellites from \citet{Wetzel2013}, who also used identical methodology, combining galaxy groups from SDSS \citep{Tinker2011, Wetzel2012} with satellite infall times (including group preprocessing) measured in mock group catalogs in their cosmological simulation.  We show their result for groups with $\mvir=10^{12-13}\msun$, which are most similar to MW/M31 masses.  Combination Combining  our results with these works suggests a complex dependence of environmental quenching timescales on satellite $\mstar$. Specifically, our results alone suggest that the quenching timescale in the MW/M31 halos increases with satellite mass, from $\lesssim1\gyr$ at $\mstar<10^7\msun$ to $\sim5\gyr$ at $\mstar\approx10^{8.5}\msun$.  However, the results of \citet{Wheeler2014} imply a doubling of the timescale to $\approx9.5\gyr$ at just higher $\mstar$, though the find no dependence in their sample from $\mstar\approx10^{8.5}$ to $10^{9.5}\msun$.  This suggests some tension with the satellite of the MW/M31.