A person standing on a platform notes that a train travelling with...

The velocity of the train is $v = 0.6c$ and the time taken to pass the observer is $t = 1 \text{ s}$.

The length of the train as measured by the observer on the platform is the contracted length $L$.

$L = v \times t = 0.6c \times 1 = 0.6 \times 3 \times 10^8 \text{ m} = 1.8 \times 10^8 \text{ m}$

According to the length contraction formula, the relation between the contracted length $L$ and the rest length $L_0$ is:

$L = L_0 \sqrt{1 - \dfrac{v^2}{c^2}}$

$L_0 = \dfrac{L}{\sqrt{1 - \dfrac{v^2}{c^2}}}$

Substituting the values of $L$ and $v$:

$L_0 = \dfrac{1.8 \times 10^8}{\sqrt{1 - (0.6)^2}}$

$L_0 = \dfrac{1.8 \times 10^8}{\sqrt{1 - 0.36}}$

$L_0 = \dfrac{1.8 \times 10^8}{0.8}$

$L_0 = 2.25 \times 10^8 \text{ m}$