Two trains of lengths 200 meters and 150 meters are running on parallel tracks in the same direction with speeds of 40 km/hr and 45 km/hr respectively. Find the time taken by the faster train to completely cross the slower train.

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Accepted Answer

To find the time taken by the faster train to cross the slower train, we need to calculate the relative speed and the total distance to be covered.

When two trains move in the same direction, the relative speed is the difference of their speeds:
$$
	ext{Relative speed} = (45 - 40) 	ext{ km/hr} = 5 	ext{ km/hr}
$$

Converting this to meters per second:
$$
5 	ext{ km/hr} = 5 	imes \frac{5}{18} 	ext{ m/sec} = \frac{25}{18} 	ext{ m/sec}
$$

The total distance to be covered equals the sum of the lengths of both trains:
$$
	ext{Total distance} = 200 + 150 = 350 	ext{ meters}
$$

Now, using the formula Time = Distance/Speed:
$$
	ext{Time taken} = 350 	imes \frac{18}{25} 	ext{ seconds} = 252 	ext{ seconds}
$$

Therefore, the faster train will take 252 seconds to completely cross the slower train.

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