We consider a congestion game with two types of agents to describe the traffic flow on a road at various time intervals in each day. The first type of agents (cars) maximize a utility which is determined by a sum of a penalty for using the road at a time other than their preferred time interval, the average velocity of the traffic flow, and the congestion tax. The second type of agents (trucks or heavy-duty vehicles) can benefit from using the road together with other second-type agents. This is because the trucks can form platoons to save fuel through reducing the air drag force. We study a Nash equilibrium of this game to study the interaction between the traffic flow and the platooning incentives. We prove that the introduced congestion game does not admit a potential function unless we devise an appropriate congestion taxing policy. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategic Nash equilibrium of this congestion game. Lastly, we demonstrate the developed results on a numerical example using data from a highway segment in Stockholm.