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A car $\text{A}$ starts from a point $\text{P}$ towards another point $\text{Q}$. Another car $\text{B}$ starts (also from $\text{P})\; 1$ hour after the first car and overtakes it after covering $30\%$ of the distance $\text{PQ}$. After that, the cars continue. On reaching $\text{Q}$, car $\text{B}$ reverses and meets car $\text{A}$, after covering $23\frac{1}{3}$ of the distance $\text{QP}$. Find the time taken by car $\text{B}$ to cover the distance $\text{PQ}$ (in hours).

1. $3$
2. $4$
3. $5$
4. $3\frac{1}{3}$

1