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• Crossing a stationary object with a reliable length: When a train crosses a stationary object
which has some length, for example, a platform, bridge, tunnel or another stationary train, it
will cover the sum of its own length and the length of the stationary object.
Example 24: A 320 m long train passes a bridge having a length of 280 m in 30 s. What is the speed
of the train in km/h?

Solution: Given, Distance (d) = length of the train + length of the bridge = 320 m + 280 m = 600 m
Time taken (t) = 30 s
d 600 m 18 18
So, the speed of the train (s) = = = 20 m/s = 20 × km/h = 72 km/h (Q 1 m/s = km/h)
t 30 s 5 5
• Crossing another moving train: When two trains cross each other, moving either in opposite
directions or the same direction, the total distance covered is the sum of their lengths.
◊ To find the time taken by two trains to cross each other, moving in opposite directions, we
add their speeds to get speed per hour.
◊ To find the time taken by the faster train to cross the slower train, moving in the same
direction, we find the difference (positive) of their speeds to get the speed per hour.

Example 25: Two trains 300 m and 200 m long, are moving at the speed of 35 km/h and 55 km/h
respectively in opposite directions. How long would it take them to pass each other?

Solution: Total distance (d) = length of the first train + length of the second train
= 300 m + 200 m = 500 m

The relative speed of two trains (s) = speed of the first train + speed of the second train
(Q Trains are moving in opposite directions)
= 35 km/h + 55 km/h = 90 km/h
5
Converting the speed from km/h to m/s, 90 km/h = 90 × 18 m/s = 25 m/s

d 500 m
Therefore, Time taken (t) = = = 20 s
s 25 m/s
Thus, the required time taken to pass each other = 20 s
Example 26: A train is 125 m long. It passes a man, running at 5 km/h in the same direction in
which the train is going. The trains takes 10 seconds to cross the man completely. Find the speed
of the train.
Solution: Given, Distance (s) = length of the train = 125 m
Time taken (t) = 10 s

Here, we will use the concept of relative speed. If two objects are moving in the same direction,
then their relative speed is equal to the difference between the two speeds.
d 125 m
So, the relative speed of the train (s) = = = 12.5 m/s
t 10 s
18 18
= 12.5 × km/h = 45 km/h (Q 1 m/s = km/h)
5 5
Since, the relative speed of the the train = speed of train – speed of the man
⇒ Speed of train – Speed of the man = 45 km/h

So, the actual speed of the train = 45 km/h + 5 km/h = 50 km/h (Q Speed of the man = 5 km/h)

293 Direct and Indirect Variations