One local and another express train were proceeding in the same direction on parallel tracks at 29 km/hour and 65 km/hour respectively. The driver of the former noticed that it took exactly 16 seconds for the faster train to pass by him. What is the lengt

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Submitted by examrobotsa on

Q: 139 (IAS/1998)
One local and another express train were proceeding in the same direction on parallel tracks at 29 km/hour and 65 km/hour respectively. The driver of the former noticed that it took exactly 16 seconds for the faster train to pass by him. What is the length of the faster train?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,5,4,1,3,5,0

keywords: 

{'faster train': [0, 1, 0, 0], 'express train': [0, 0, 0, 1], 'parallel tracks': [0, 1, 0, 0], 'length': [0, 0, 1, 0], 'km': [0, 0, 2, 1], 'seconds': [3, 3, 8, 6], 'hour': [5, 5, 11, 12]}

To find the length of the faster train, we can use the relative speed concept.

The relative speed between the two trains is the difference of their speeds:

Relative speed = Speed of express train - Speed of local train

Relative speed = 65 km/h - 29 km/h = 36 km/h

We need to convert the relative speed from km/h to m/s since the time given is in seconds.

1 km/h = (5/18) m/s

Relative speed = 36 km/h * (5/18) m/s = 10 m/s

We are given that it took 16 seconds for the faster train to pass the driver of the local train. The time it takes for the train to pass is the same as the time it takes for the train to cover its own length.

Distance = Speed * Time

Length of faster train = Relative speed * Time

Length of faster train = 10 m/s * 16 s = 160 meters

Therefore, the length of the faster train is 160 meters.