A train, 150 m long, takes 30 seconds to cross a bridge 500 m long. How much time will the train take to cross a platform 370 m long?

### Concept & Formula When a train crosses an object with length, the total distance covered is the sum of the train's length and the object's length. First, calculate the speed of the train from the bridge scenario, and use it for the platform scenario. $$ \text{Speed} = \frac{\text{Total Distance}}{\text{Time}} $$ ### Step-by-Step Solution * **Given:** * Length of train = $150$ m. * Length of bridge = $500$ m. * Time to cross bridge = $30$ seconds. * Length of platform = $370$ m. * **Calculation:** * Total distance for bridge = $150 + 500 = 650$ m. * Speed of train = $\frac{650}{30} = \frac{65}{3}$ m/s. * Total distance for platform = $150 + 370 = 520$ m. * Time to cross platform = $\frac{\text{Distance}}{\text{Speed}} = \frac{520}{\frac{65}{3}}$ seconds. * Time = $520 \times \frac{3}{65} = 8 \times 3 = 24$ seconds. ### Exam Strategy & Shortcut Since speed is constant, the ratio of distances equals the ratio of times. Distance 1 = $650$ m, Time 1 = $30$ s. Distance 2 = $520$ m, Time 2 = $t$. $\frac{650}{30} = \frac{520}{t} \Rightarrow t = \frac{520 \times 30}{650} = \frac{52 \times 3}{6.5} = 24$ seconds. ### Common Pitfall A common mistake is forgetting to add the train's length to the platform's length when finding the second distance. ### Final Answer Therefore, the correct answer is **24 sec**.