One train is 185 m longer than the other train. When they move in opposite direction they cross each other in 25 sec. When they move in same direction the faster train crosses the slower train in 75 sec. If the speed of slower train is 20 km/hr then what is the speed of faster train.

40 km/hr

Let the length of a train is x m and (180 + x)m & the speed of faster train is S km/h

ATQ,

When train moves in opposite direction

\(\frac{180+x+x}{S+20}\) = \(\frac{25}{60 × 60}\)  ------ (i)

When train moves in same direction

\(\frac{180+x+x}{S -20}\) = \(\frac{75}{60 × 60}\)  ------ (ii)

From eqn (i) & (ii)

\(\frac{25(S+20)}{60 × 60}\) = \(\frac{75(S-20)}{60 × 60}\)

S + 20 = 3(S-20)

S + 20 = 3S - 60

      2S = 80 ⇒ S = 40 km/h