A passenger sitting in a train A moving at 90   km   h - 1 observes another train B moving in the…

Let the velocity of A be $v_A$ and the velocity of B be $v_B$.

The relative velocity is

$$\begin{gathered} {\overrightarrow{v}}_{BA} ={\overrightarrow{v}}_B-{\overrightarrow{v}}_A \\ \Rightarrow v_{BA}= 54-(-90)=144 \mathrm{km} {\mathrm{h}}^{-1} \end{gathered}$$

$\Rightarrow v_{BA}= 40 \mathrm{m} {\mathrm{s}}^{-1}$

$\mathrm{Time}=\frac{\mathrm{length}}{v_{BA}}$ 

$\Rightarrow \mathrm{length}= 40 \mathrm{m} {\mathrm{s}}^{-1} \times 8 \mathrm{s}=320 \mathrm{m}$