Train A crosses a stationary train B in 50 seconds and a pole in 20 seconds with the same speed. The length of the train A is 240 metres. What is the length of the stationary train B?

### Concept & Formula The speed of Train A can be found using the time it takes to cross a pole (a point object), where Distance = Length of Train A. $$ \text{Speed} = \frac{\text{Length of Train A}}{\text{Time to cross pole}} $$ ### Step-by-Step Solution * **Given:** * Length of Train A = $240$ m. * Time to cross pole = $20$ seconds. * Time to cross stationary Train B = $50$ seconds. * **Calculation:** * Speed of Train A = $\frac{240}{20} = 12$ m/s. * Total distance to cross Train B = Length of Train A + Length of Train B. * Total distance = $\text{Speed} \times \text{Time} = 12 \times 50 = 600$ m. * Length of Train B = Total distance - Length of Train A. * Length of Train B = $600 - 240 = 360$ m. ### Exam Strategy & Shortcut Train A takes $20$s to cross its own length. It takes $50$s to cross its own length + Train B. Thus, it takes $30$s ($50 - 20$) just to cross the length of Train B. Since its speed is $\frac{240}{20} = 12$ m/s, Length of Train B = $12 \times 30 = 360$ m. ### Common Pitfall Students might divide the total distance by $2$ or mistakenly assume Train B is moving and apply relative speed formulas. Read carefully that Train B is "stationary." ### Final Answer Therefore, the correct answer is **360 metres**.