Two trains one 500 meters long and the other 1000 meters lon

Two trains, one 500 meters long and the other 1000 meters long, are traveling in opposite directions on parallel tracks. The first train is traveling at 100km/h and the other at 80km/h. How long will it take for the trains to pass each other from the moment the locomotives are at the same point?

Solution

The diagram as below.
500 m 100 km/h ->
A<------>B (1st train)
C<------------->D (2nd train)
<- 80 km/h 1000 m
When they pass each other after t hrs,diagram as
A B
<------>
<------------->
C D
After t hrs, B moves 100 t km and C moves 80 t km.
So we have 100 t + 80 t = BC = CD + AB = 1000+ 500
So, 180 t = 1500, t = 25/3 hrs
[Or get t by (1000+ 500)/(100+80) directly.
Answer: it takes 25/3 hrs for the trains to pass each other
from the moment the locomotives are at the same point.
Or get t by (1000 + 500)/ (1000+ 60) directly.