A train that is 150 meters long crosses a platform that is 300 meters long in 45 seconds daily. Chirag, a passenger on board the train today, is standing in the last compartment and starts moving towards the engine of the train at a speed of 18 km/h exactly when the train is about to start crossing the platform. How long (in seconds) would Chirag take to cross the platform?
Question
A train that is 150 meters long crosses a platform that is 300 meters long in 45 seconds daily. Chirag, a passenger on board the train today, is standing in the last compartment and starts moving towards the engine of the train at a speed of 18 km/h exactly when the train is about to start crossing the platform. How long (in seconds) would Chirag take to cross the platform?
Solution
First, let's find out the speed of the train.
The total distance covered by the train to cross the platform is the length of the train plus the length of the platform, which is 150 meters + 300 meters = 450 meters.
The train crosses this in 45 seconds. So, the speed of the train is Distance/Time = 450 meters / 45 seconds = 10 meters/second.
Now, let's convert Chirag's speed from km/h to m/s. 1 km/h is equal to 5/18 m/s. So, 18 km/h = 18 * (5/18) = 5 m/s.
Chirag is moving in the same direction as the train. So, his effective speed relative to the platform is the speed of the train plus his own speed, which is 10 m/s + 5 m/s = 15 m/s.
The distance Chirag needs to cover is the length of the platform, which is 300 meters.
So, the time Chirag would take to cross the platform is Distance/Speed = 300 meters / 15 m/s = 20 seconds.
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