Two trains 120 m and 80 m in length are running in opposite directions with velocities 42 km/h and 30 km/h respectively.

Given: l₁ = 120 m, l₂ = 80 m,

v_A = 42 km/h = 42 × \(\frac{5}{18}=\frac{35}{3}\) m/s,

v_B = -30km/h= -30 × \(\frac{5}{18}=\frac{-25}{3}\) m/s

To find: Time taken by trains to cross each other (t)

Formula: Time = \(\frac{Distance}{speed}\)

Calculation : Total distance to be travelled

= sum of lengths of two trains

= 120 + 80 = 200m

Relative velocity of A with respect to B is v_AB,

v_AB = v_A – v_B

= \(\frac{35}{3}-(\frac{-25}{3})\)

= \(\frac{60}{3}\)

∴ v_AB = 20m/S

From formula,

∴ Time taken to cross each other (t) = \(\frac{Distance}{speed}\)

= \(\frac{200}{20}\)

= 10 s

Time taken by the two trains to cross each other is 10 s.