Two trains of length 100 meter and 80 meter are running on parallel track . If they run in same direction they cross each other in 18 sec. and in opposite direction they cross each other in 9 sec . The speed of faster train is :

15 m/sec

Total length = length of train 1   + length of train 2 

                 =   ( 100 + 80 )m = 180m

Speed of train 1 = x m/sec , speed of train 2 = y m/sec

When they move in same direction , relattive speed = (  x - y ) m/sec

Time = 18 sec 

Relative speed  ( x - y ) = \(\frac{180}{18}\)  = 10 m/sec  -------- ( 1 )

When they move in opposite direction , relative speed = ( x + y ) m/sec

Time = 9 sec 

Relative speed ( x + y ) = \(\frac{180}{9}\) = 20 m/sec    ------ ( 2 ) 

Add equation 1 and equation 2 

2x = 30 

x = 15 m/sec , y = 5 m/sec 

Speed of faster train = 15 m/sec