  In this paper we study a ratio-dependent predator-prey model with a free
boundary causing by both prey and predator over a one dimensional habitat. We
study the long time behaviors of the two species and prove a
spreading-vanishing dichotomy, namely, as t goes to infinity, both prey and
predator successfully spread to the whole space and survive in the new
environment, or they spread within a bounded area and die out eventually. Then
the criteria governing spreading and vanishing are obtained. Finally, when
spreading occurs, we provide some estimates to the asymptotic spreading speed
of h(t).
