We combine orbital information from N-body simulations with an analytic model for star formation quenching and SDSS observations to infer the differential effect of the group/cluster environment on star formation in satellite galaxies. We also consider a model for gas stripping, using the same input supplemented with HI fluxes from the ALFALFA survey. The models are motivated by and tested on the Hydrangea cosmological hydrodynamical simulation suite. We recover the characteristic times when satellite galaxies are stripped and quenched. Stripping in massive ($M_mathrm{ vir}sim 10^{14.5},mathrm{M}_odot$) clusters typically occurs at or just before the first pericentric passage. Lower mass ($sim10^{13.5},mathrm{M}_odot$) groups strip their satellites on a significantly longer (by $sim3,mathrm{Gyr}$) timescale. Quenching occurs later: Balmer emission lines typically fade $sim3.5,mathrm{Gyr}$ ($5.5,mathrm{Gyr}$) after first pericentre in clusters (groups), followed a few hundred $mathrm{Myr}$ later by reddenning in $(g-r)$ colour. These `delay timescales are remarkably constant across the entire satellite stellar mass range probed ($sim10^{9.5}-10^{11},mathrm{M}_odot$), a feature closely tied to our treatment of `group pre-processing. The lowest mass groups in our sample ($sim10^{12.5},mathrm{M}_odot$) strip and quench their satellites extremely inefficiently: typical timescales may approach the age of the Universe. Our measurements are qualitatively consistent with the `delayed-then-rapid quenching scenario advocated for by several other studies, but we find significantly longer delay times. Our combination of a homogeneous analysis and input catalogues yields new insight into the sequence of events leading to quenching across wide intervals in host and satellite mass.
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