A train passes a 500m long platform in 12 seconds and a man standing on the platform in 4 seconds. Find the speed of the train.

Let the length of the train be Lmeters and its speed be vm/s.
When passing a standing man, the train covers its own length:

Speed (v)=
Time
Length of train
​
=
4
L
​
⟹L=4v
When passing the platform, the train covers its own length plus the length of the platform:

Speed (v)=
12
L+500
​

Substitute L=4v into the second equation:

v=
12
4v+500
​

12v=4v+500
8v=500
v=
8
500
​
=62.5m/s
Convert the speed from m/s to km/h:

Speed in km/h=62.5×
5
18
​
=12.5×18=225km/h