A train passes two bridges 400m and 295m long in 75 seconds and 60 seconds respectively. How much time (in seconds) will the train take to cross another train of length 325m running on parallel tracks at the speed of 97.2km/h in the same direction?

Let the length of the train be L and its speed be v.
From the first two cases:

v=
75
L+400
​
=
60
L+295
​

Cross-multiply to solve for L:

60(L+400)=75(L+295)
4(L+400)=5(L+295)
4L+1600=5L+1475
L=1600−1475=125m
Now find the speed v:

v=
75
125+400
​
=
75
525
​
=7m/s
Convert the speed of the second train to m/s:

v
2
​
=97.2km/h=97.2×
18
5
​
=5.4×5=27m/s
Since they are running in the same direction, the relative speed is:

Relative Speed=v
2
​
−v=27−7=20m/s
Total distance to be covered to cross each other:

Total Distance=L
1
​
+L
2
​
=125+325=450m
Time taken:

Time=
Relative Speed
Total Distance
​
=
20
450
​
=22.5=22
2
1
​
 seconds