This work considers an existing system of differential equations based on Huygens' Principle that can, under some assumptions, trace the position in time of the perimeter of a large wildland fire. These equations in general require a sophisticated numerical solution, however it is demonstrated that if fuel and meteorological conditions are functions of time only, then an analytic solution can be obtained to the equations. The solution is in the form of a definite integral involving the affecting variables expressed as functions of time. For the special case of only time dependent wind velocity, the solution is presented in terms of probability distributions. The solution allows an analysis of its properties giving an insight into the behaviour of wildland fire.