Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is

### Concept & Logic When objects move in opposite directions, you add their speeds to find the relative speed. Since the lengths are already given in kilometers and speeds in km/hr, it is fastest to calculate the time in hours first, then convert directly to seconds. $$ \text{Relative Speed} = S_1 + S_2 $$ ### Step-by-Step Solution * **Given:** * Speed of train 1 = $60$ km/hr. * Speed of train 2 = $90$ km/hr. * Length of train 1 = $1.10$ km. * Length of train 2 = $0.9$ km. * **Calculation:** * Relative speed = $60 + 90 = 150$ km/hr. * Total distance = $1.10 + 0.9 = 2.0$ km. * Time in hours = $\frac{\text{Distance}}{\text{Relative Speed}} = \frac{2}{150}$ hours. * Convert time to seconds: $\frac{2}{150} \times 3600 = \frac{2 \times 360}{15} = \frac{720}{15}$. * $720 \div 15 = 48$ seconds. ### Exam Strategy & Shortcut Keep units consistent to save time. Total distance is exactly $2$ km. Relative speed is $150$ km/hr. Time is $\frac{2}{150}$ hr. Multiply by $3600$ to get seconds: $\frac{7200}{150} = \frac{720}{15} = 48$. No need to convert km/hr to m/s or km to meters! ### Common Pitfall A time-wasting pitfall is converting all km values to meters and km/hr to m/s right at the start. While it works, it introduces unnecessary arithmetic steps that increase the chance of calculation errors. ### Final Answer Therefore, the correct answer is **48**.