A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

### Concept & Formula When two bodies move in opposite directions, their relative speed is the sum of their individual speeds. Since a man is considered a point object, the distance to be covered is simply the length of the train. $$ \text{Relative Speed} = V_{\text{train}} + V_{\text{man}} $$ ### Step-by-Step Solution * **Given:** * Length of train = $110$ m. * Speed of train = $60$ kmph. * Speed of man = $6$ kmph. * **Calculation:** * Relative speed = $60 + 6 = 66$ kmph. * Convert to m/s: $66 \times \frac{5}{18} = \frac{330}{18} = \frac{55}{3}$ m/s. * Total distance = $110$ m. * Time taken = $\frac{\text{Distance}}{\text{Relative Speed}} = \frac{110}{\frac{55}{3}}$ seconds. * Time = $110 \times \frac{3}{55} = 2 \times 3 = 6$ seconds. ### Exam Strategy & Shortcut Instead of fully simplifying $\frac{330}{18}$, you can write the time equation as $\frac{110 \times 18}{330}$. The $110$ goes into $330$ exactly $3$ times, leaving $\frac{18}{3} = 6$ seconds. ### Common Pitfall Students often subtract the speeds by mistake out of habit. Always look for the keyword "opposite" to remind yourself to add the speeds together. ### Final Answer Therefore, the correct answer is **6 sec**.