A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

### Concept & Relative Speed When two bodies move in the same direction, their relative speed is the difference between their individual speeds. To completely pass the jogger, the train must cover the initial distance gap plus its own entire length. $$ \text{Relative Speed} = V_{\text{train}} - V_{\text{jogger}} $$ $$ \text{Total Distance} = \text{Initial Gap} + \text{Length of Train} $$ ### Step-by-Step Solution * **Given:** * Speed of jogger = $9$ kmph. * Speed of train = $45$ kmph. * Initial gap = $240$ m. * Length of train = $120$ m. * **Calculation:** * Relative speed = $45 - 9 = 36$ kmph. * Convert to m/s: $36 \times \frac{5}{18} = 10$ m/s. * Total distance the train needs to cover relative to the jogger = $240 + 120 = 360$ m. * Time taken = $\frac{\text{Total Distance}}{\text{Relative Speed}} = \frac{360}{10} = 36$ seconds. ### Exam Strategy & Shortcut Instantly convert the relative speed of $36$ kmph to $10$ m/s. Add the gap and the train's length ($360$ m) in your head. Divide $360$ by $10$ to get $36$ seconds immediately. ### Common Pitfall A very common mistake is only calculating the time required to cover the $240$m gap, forgetting that the train must also advance its own $120$m length past the jogger to completely "pass" him. ### Final Answer Therefore, the correct answer is **36 sec**.