A 280-metre long train crosses a platform thrice its length in 50 seconds. What is the speed of the train in km/hr?

### Concept & Formula The total distance covered by the train to cross the platform is the sum of the train's length and the platform's length. $$ \text{Total Distance} = L_{\text{train}} + L_{\text{platform}} $$ ### Step-by-Step Solution * **Given:** * Length of the train ($L$) = $280$ m * Length of the platform = $3 \times 280 = 840$ m * Time taken ($T$) = $50$ seconds * **Calculation:** * Total distance = $280 + 840 = 1120$ m. * Speed in m/s = $\frac{1120}{50} = \frac{112}{5}$ m/s. * Convert to km/hr = $\frac{112}{5} \times \frac{18}{5} = \frac{2016}{25}$. * $\frac{2016}{25} = \frac{2016 \times 4}{100} = \frac{8064}{100} = 80.64$ km/hr. ### Exam Strategy & Shortcut Instead of calculating $3 \times 280$ and adding $280$, recognize that the total length is simply $4$ times the train's length ($4 \times 280 = 1120$). When dividing by $25$, multiply the numerator by $4$ and place the decimal two spots to the left. ### Common Pitfall Students might calculate the platform's length as $3 \times 280$ but forget to add the train's original length when determining the total distance covered. ### Final Answer Therefore, the correct answer is **80.64**.