Two trains 180 m and 120 m long respectively pass each other in 54 seconds when they run in the same direction and in 18 seconds when run in opposite directions. Find the speed of first train.

Question: Two trains 180 m and 120 m long respectively pass each other in 54 seconds when they run in the same direction and in 18 seconds when run in opposite directions. Find the speed of first train.

Solution:
Let the speed of 1st train is S1 and speed of 2nd train is S2
Time = total distance/ relative speed

1) In same direction
54 = (180 + 120)/(S1 - S2) × (5/18)
⇒ (S1 - S2)54 = (300 × 18)/5
⇒ (S1 - S2) = 20

2) In opposite direction
18 = (180 + 120) / (S1 + S2) × (5/18)
⇒ (S1 + S2)18 = (300 × 18)/5
⇒ (S1 + S2) = 60

from 1 and 2
S1 = 40 km/hr