The main goal of this paper is to better understand the route lifetime dynamics in Intervehicle communication networks (IVC) or what we call intervehicle mobile ad hoc networks (iv-MANETs) that are a special class of MANETs but exhibit very different behavior from them. We consider the problem of finding an optimal multi-hop route between two vehicular nodes in an iv-MANET. For a given choice of the number of hops and distances between intermediate nodes, we seek the characterizing properties of choice of speeds of the intermediate nodes so as to maximize the expected lifetime of the multi-hop route. Our analytical model inherently incorporates the randomly changing speeds of nodes over time and hence the optimal choice depends on the dynamics of the stochastic process corresponding to the speed of the nodes. We suppose that for establishing a route the locations and speeds of other vehicles are known. Under a markovian assumption on the process of the speed of nodes, we show that the optimal choice of speeds attempts to equalize the lifetimes of adjacent links in a route. A monotone variation property of the speed of the intermediate nodes under the optimal policy is proved. These solution structures have been confirmed with an extensive simulation study. The heuristics and structures developed in this paper can serve in designing a new set of efficient interactive routing protocols specifically tailored for high mobility ad hoc networks and iv-MANETs in particular.