  Several lines of evidence have suggested that the the galaxy cluster
Cl~0024+17, an apparently relaxed system, is actually a collision of two
clusters, the interaction occurring along our line of sight. In this paper we
present a high-resolution $N$-body/hydrodynamics simulation of such a
collision. We have created mock X-ray observations of our simulated system
using MARX, a program that simulates the on-orbit performance of the Chandra
X-ray Observatory. We analyze these simulated data to generate radial profiles
of the surface brightness and temperature. At later times, $t = 2.0-3.0$ Gyr
after the collision, the simulated surface brightness profiles are better fit
by a superposition of two $\beta$-model profiles than a single profile, in
agreement with the observations of Cl~0024+17. In general, due to projection
effects, much of the post-collision density and temperature structure of the
clusters is not seen in the observations. In particular, the observed
temperatures from spectral fitting are much lower than the temperature of the
hottest gas. We determine from our fitted profiles that if the system is
modeled as a single cluster, the hydrostatic mass estimate is a factor
$\sim$2-3 less than the actual mass, but if the system is modeled as two galaxy
clusters in superposition, a hydrostatic mass estimation can be made which is
accurate to within $\sim$10%. We examine some implications of these results for
galaxy cluster X-ray surveys.
