One train is 250 m longer than the other train . When they move in opposite direction they cross each other in 19 seconds and when they move in same direction they take \(\frac{5}{3}\) times time. If speed of faster train is 36 km/hr then find the speed of slower train .

9 km/hr

Distance = Speed × Time 

Ratio of time taken by trains when they move in same direction to the time taken when they move in opposite direct 

Ratio             Opposite direction  :    Same direction

                                 19          :         19 × \(\frac{3}{5}\) 

                                  5           :          3 

Let speed of faster train = F km/hr 

 and speed of slower train = S km/hr 

Relative speed when trains move in opposite direction = ( F + S ) = 5R

Relative speed when trains move in same direction = ( F - S ) = 3R

 F = \(\frac{5R \; +  \;3R}{2}\)  = 4R 

 S = \(\frac{5R \; -  \;3R}{2}\)  = 1R 

Ratio of speed of faster train to slower train , 

Ratio        F    :    S 

               4    :    1

According to question ,   4R = 36 km/hr   ⇒  1R = 9 km/hr 

speed of slower tain = 9 km/hr