= Solution
Apply <flow conservation> at the four junctions, using the directions in the original diagram:
$$
\begin{array}{rcll}
F_4+150&=&F_1& (A),\\
F_1&=&F_2+200& (B),\\
F_2+100&=&F_3& (C),\\
F_3&=&F_4+50& (D).
\end{array}
$$
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 yields
$$
\boxed{(F_1,F_2,F_3,F_4)=(200+t,t,100+t,50+t),\qquad t\ge0,}
$$
in cars per hour. The <nonnegativity> restriction expresses clockwise traffic on every arc. Conversely, every $t\ge0$ 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.
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