A train, 250 m long, passes a railway platform 200 m long, in 45 s with a uniform speed. What is the time (in seconds) taken by the train to pass a man cycling in the direction of the train at a speed of 6 km/h?

Step 1: Find the speed of the train.
Total distance covered while crossing the platform = Length of train+Length of platform

Distance=250+200=450 m
Time=45 s
Speed of train (V
t
​
)=
Time
Distance
​
=
45
450
​
=10 m/s
Convert speed into km/h:

V
t
​
=10×
5
18
​
=36 km/h
Step 2: Find relative speed when passing the cyclist.
Speed of the cyclist (V
c
​
) = 6 km/h (in the same direction)

Relative Speed=V
t
​
−V
c
​
=36−6=30 km/h
Convert relative speed back to m/s:

Relative Speed in m/s=30×
18
5
​
=
3
25
​
 m/s
Step 3: Calculate the time taken to cross the man.
To cross the man, the train needs to cover its own length (250 m).

Time=
Relative Speed
Length of train
​
=
3
25
​

250
​
=250×
25
3
​
=30 s