 Solution

Apply flow conservation at the four junctions, using the directions in the original diagram:The total external inflow and outflow are both 250 cars per hour. Accordingly one of these linear equations is redundant. Put $F_2=t$. Successive substitution yieldsin cars per hour. The nonnegativity restriction expresses clockwise traffic on every arc. Conversely, every $t\ge 0$ gives nonnegative flows satisfying all four conservation equations, so this is the whole physically allowable family. Increasing $t$ adds a common network circulation around the roundabout without changing any external inflow or outflow.