Two trains, one of length 210 m and 250 m are running on parallel tracks in opposite directions with speeds \( 130 \mathrm{~km} / \mathrm{hr} \) and \( 110 \mathrm{~km} / \mathrm{hr} \) . How long will it take for them to cross other completely?
1. Find the Total Distance to be Covered - For two trains to completely cross each other, the total distance is the sum of their lengths.
- Total Distance = 210 m + 250 m = 460 m.
2. Find the Relative Speed - Since the trains are moving in opposite directions, their relative speed is the sum of their individual speeds.
- Relative Speed = 130 km/hr + 110 km/hr = 240 km/hr.
3. Convert Speed to m/s - To ensure our units are consistent (meters and seconds), we convert the speed from km/hr to m/s by multiplying by 5/18.
- Speed in m/s = 240 × (5/18) = 200/3 m/s.
4. Calculate the Time to Cross - The time taken is the total distance divided by the relative speed.
- Time = Total Distance ÷ Relative Speed
- Time = 460 ÷ (200/3) = (460 × 3) / 200
- Time = 1380 / 200 = 6.9 seconds.
Final Answer: It will take 6.9 seconds for the trains to cross each other completely.
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