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A train running at a certain speed crosses a person running towards it at a speed of 6 km/hr in 18 seconds and takes 30 seconds to cross a platform on its way of length 160 m. What is the speed (in km/hr) of the train?
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A train running at a certain speed crosses a person running towards it...
Given data:
- Speed of the person (P) = 6 km/hr
- Time taken by the person to cross the train = 18 seconds
- Length of the platform (L) = 160 m
- Time taken by the train to cross the platform = 30 seconds

Calculating the speed of the train:
To find the speed of the train, we need to determine the distance covered by the train while crossing the person and the platform.

Distance covered while crossing the person:
Let's assume the length of the train (T) is 'x' meters.
The relative speed between the train and the person is the sum of their individual speeds.
Relative speed = Speed of the train - Speed of the person
Relative speed = T/18 m/s = (T/18)(18/5) km/hr = (T/5) km/hr
Relative speed = Speed of the train - 6 km/hr

Since both the train and the person are running towards each other, the relative speed is the sum of their individual speeds.
Relative speed = Speed of the train + Speed of the person
Therefore, (T/5) = Speed of the train + 6

Distance covered while crossing the platform:
The length of the train (T) is the distance covered by the train while crossing the platform.
T = 160 m

Equating the distances:
The distance covered while crossing the person is equal to the distance covered while crossing the platform.
(T/5) km/hr = T m/30 s

Solving for T:
(T/5) = (T/30)(18/5)
6T = 18T
12T = 0
T = 0

Conclusion:
The length of the train (T) comes out to be zero, which is not possible. Hence, there is an error in the given data or the problem statement. Without the length of the train, we cannot calculate the speed of the train.
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A train running at a certain speed crosses a person running towards it at a speed of 6 km/hr in 18 seconds and takes 30 seconds to cross a platform on its way of length 160 m. What is the speed (in km/hr) of the train?
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