 Solution

Using the same luminosity estimate, the distance modulus is $12.5-(-22.49)=34.99$, implying $D\simeq 99.4$ Mpc. Pure Hubble expansion at that distance predicts about $7450\mathrm{km}{\mathrm{s}}^{-1}$. The measured velocity therefore impliesIts line-of-sight peculiar velocity is toward us, of the order expected for orbital motions in a rich galaxy cluster. A galaxy falling toward a cluster centre from its far side could have this sign. Its actual front/back location or three-dimensional orbit is not determined without the cluster's mean velocity, distance and projected position. Tully-Fisher scatter and the assumption of identical luminosities also limit that inference.