The velocity dependent transport equation for a nonabsorbing semi-infinite medium with no sources is approximately solved by a variational method. A simple trial function, which takes into account the asymptotic behavior of the exact solution, is used to obtain an approximation for the extrapolation distance q, and, by iteration, an approximation for the flux distribution. Numerical results are given for a monatomic gaseous medium with the atom mass equal to the neutron mass. The value q = 0.9345 l (∞) is obtained. The velocity distribution of the emerging neutrons shows a hardening effect, corresponding, in the average, to a 14% increase in the neutron temperature.