A train of length 180 metres crosses a tree in 15 seconds and crosses another train of the same length travelling in opposite direction in 20 seconds. What is the speed (in km/hr) of the second train?

1. Let the speed of the first train be v
1
​
.
When it crosses a tree, the distance covered is its own length (180 m):

v
1
​
=
Time
Distance
​
=
15
180
​
=12 m/s
Let the speed of the second train be v
2
​
.
When crossing each other in opposite directions, the relative speed is v
1
​
+v
2
​
, and the total distance covered is the sum of their lengths (180+180=360 m):

v
1
​
+v
2
​
=
Time
Total Distance
​
=
20
360
​
=18 m/s
Substitute v
1
​
=12 m/s into the equation:

12+v
2
​
=18⟹v
2
​
=6 m/s
Convert the speed of the second train into km/hr:

Speed in km/hr=v
2
​
×
5
18
​
=6×
5
18
​
=
5
108
​
=21.6 km/hr