Identify Given Parameters

Note down the length of the train $L_t = 150\text{ m}$, the length of the platform $L_p = 250\text{ m}$, and the speed of the train $v = 54\text{ km/h}$.

$L_t = 150\text{ m}, \quad L_p = 250\text{ m}, \quad v = 54\text{ km/h}$

Convert Speed to m/s

Convert the speed from km/h to m/s by multiplying by $\frac{5}{18}$.

$v = 54 \times \frac{5}{18} = 15\text{ m/s}$

Calculate Total Distance

To cross a platform, the total distance to cover is the sum of the length of the train and the length of the platform.

$D = 150 + 250 = 400\text{ m}$

Calculate Time Required

Use the formula for time $t = \frac{\text{Distance}}{\text{Speed}}$ to find the total time taken.

$t = \frac{400}{15} = \frac{80}{3} \approx 26.6\text{ seconds}$