4. 212 The river water is flowing, entering a still lake at point $Q$, a swimmer travels downstream from $P$ to $Q$, then across the lake to $R$, taking a total of 3 hours. If he travels from $R$ to $Q$ and then to $P$, it takes a total of 6 hours. If the lake water also flows, at the same speed as the river, then traveling from $P$ to $Q$ and then to $R$ would take $\frac{5}{2}$ hours. Under these conditions, how long would it take to travel from $R$ to $Q$ and then to $P$?
[Solution] Let the swimmer's speed be 1, the water speed be $y$, $P Q=a$, $Q R=b$, then
$$\left\{\begin{array}{l}
\frac{a}{1+y}+b=3 \\
\frac{a+b}{1+y}=\frac{5}{2} \\
\frac{a}{1-y}+b=6 .
\end{array}\right.$$
(1) - (2) gives $\frac{b y}{1+y}=\frac{1}{2}$, i.e., $b=\frac{1+y}{2 y}$.
(3) - (1) gives $\frac{a \cdot 2 y}{1-y^{2}}=3$, i.e., $a=\frac{3\left(1-y^{2}\right)}{2 y}$.

From (2), (4), and (5) we get
$$\frac{5}{2}(1+y)=a+b=\frac{1+y}{2 y} \cdot(4-3 y) .$$

i.e.,
$$5 y=4-3 y$$

Thus, $y=\frac{1}{2}$,
$$\frac{a+b}{1-y}=\frac{a+b}{1+y} \times \frac{1+y}{1-y}=\frac{5}{2} \times \frac{1+\frac{1}{2}}{1-\frac{1}{2}}=\frac{15}{2} \text { (hours). }$$