Urban street networks exhibit hypercongested traffic states in which flow and speed drop as vehicles crowd the network. An important feature of aggregate traffic models based on the macroscopic fundamental diagram is that the dynamics of congestion are represented in a physically realistic way. For peak demand in a city in which all travelers use cars, hypercongested states are known to be unstable in equilibrium. In real cities travelers are able to choose whether to use cars or public transit during a peak period. This paper presents a model of the equilibrium for cars and transit, recognizing that hypercongestion often arises when modes are not priced. It is shown that hypercongested traffic can be part of a stable, steady equilibrium state when cars and high-capacity transit are used simultaneously. The paper also shows that coordinated fixed prices for cars and transit can always prevent hypercongested traffic states from developing.