This paper proposes coupling the Pipes car-following model with the GM model to formulate a new car-following model that can generate consistent separation distances between the leading and following vehicles. First, an example is given to show that the GM car-following model can lead to different separation distances at the same steady speed. Secondly, a new model is formulated by coupling the Pipes model with the GM model and it is shown that the only meaningful attractor of the new model is one producing consistent separation distances at the same steady speed. Furthermore, the relationship of those macroscopic traffic flow quantities inherent in the new car-following model has also been investigated. In the steady state, the resulting speed-density relationship is exactly the same as one derived from the Pipes model. In the dynamic case, the derived speed-density relationship is a partial differential equation. Numerical experiments are carried out to show that the new car-following model can generate consistent separation distances between the leading and following vehicles.