A train, 150 meters long, takes 30 seconds to cross a bridge that is 500 meters long. How much time will it take for the same train to cross a platform that is 370 meters long?

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Accepted Answer

The speed of the train can be calculated using the formula:  
$$
	ext{Speed} = \frac{	ext{Distance}}{	ext{Time}}
$$

While crossing the bridge, the total distance covered by the train is the sum of its length and the length of the bridge:  
$$
	ext{Total Distance} = 	ext{Length of Train} + 	ext{Length of Bridge} = 150 \, 	ext{m} + 500 \, 	ext{m} = 650 \, 	ext{m}.
$$

The time taken to cross the bridge is given as 30 seconds. Thus, the speed of the train is:  
$$
	ext{Speed} = \frac{	ext{Total Distance}}{	ext{Time}} = \frac{650}{30} = \frac{65}{3} \, 	ext{m/s}.
$$

Now, calculate the time required to cross a platform. The total distance covered while crossing the platform is:  
$$
	ext{Total Distance} = 	ext{Length of Train} + 	ext{Length of Platform} = 150 \, 	ext{m} + 370 \, 	ext{m} = 520 \, 	ext{m}.
$$

Using the speed calculated earlier:  
$$
	ext{Time Taken} = \frac{	ext{Total Distance}}{	ext{Speed}} = \frac{520}{\frac{65}{3}} = 520 	imes \frac{3}{65}.
$$

Simplify the calculation:  
$$
520 	imes \frac{3}{65} = 24 \, 	ext{s}.
$$

Therefore, the time taken by the train to cross the platform is **24 seconds**.

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