A goods train, travelling at constant speed, crossed two persons walking in the same direction (as that of the train) in 11.6 seconds and 11.8 seconds, respectively. The first person was walking at 5.85 km/h, while the second was walking at 6.3 km/h. What was the speed of the train (in km/h)?

Let the speed of the train be v km/h and the length of the train be L km.
When a train crosses a moving person, the distance covered equals the length of the train, and the relative speed is used. Since they move in the same direction:

For the first person:

Relative speed=(v−5.85) km/h
Time=11.6 seconds=
3600
11.6
​
 hours
L=(v−5.85)×
3600
11.6
​

For the second person:

Relative speed=(v−6.3) km/h
Time=11.8 seconds=
3600
11.8
​
 hours
L=(v−6.3)×
3600
11.8
​

Equating both expressions for L:

(v−5.85)×
3600
11.6
​
=(v−6.3)×
3600
11.8
​

(v−5.85)×11.6=(v−6.3)×11.8
11.6v−67.86=11.8v−74.34
11.8v−11.6v=74.34−67.86
0.2v=6.48
v=
0.2
6.48
​
=32.4 km/h