Basic Train Problems

In this class, We discuss Basic Train Problems.

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Example 1:

A train is moving at a speed of 132 kmph.

Suppose the length of the train is 110 meters. How long will it take to cross a railway platform of length 165 meters long?

Solution:

The below diagram shows the graphical intuition for the formula.

To cross the platform train has to move a length of train and platform.

Distance = (110 + 165) = 275 meters

speed = 132 kmph = 132 *(5/18) = 110/3 m/s

Time = Distance / Speed

Time = 275/ (110/3) = 15/2 sec = 7 1/2 second.

Example 2:

A man is standing on a railway bridge which is 180 meters long.

The man finds a train crossing a bridge in 20 seconds and passing himself in 8 seconds.

Find the length of the train and its speed?

Solution:

The below diagram shows the graphical intuition of the question.

To cross the bridge train has to travel the length of the bridge and the length of the train.

To pass a man train has to travel the length of the train.

Length of the train = x

speed = distance / time

s = (x + 180)/20

s = x/8

x/8 = (x + 180)/20

x = 120 = length of the train

speed = 120/8 m/s

Example 3:

The length of the bridge, which a train 130 meters long and travelling at a speed of 45 kmph can cross in 30 seconds, is?

Solution:

The below diagram shows the graphical intuition of the question.

Speed = 45 kmph = 45 * 5/18 = 25/2 m/s

t = 30 second.

distance = 130 + x where x = length of bridge.

distance = speed * time

130 + x = (25/2) * 30

x = 245 meters.