(16) A train 170 m long is running with a speed of  72 kmph. In what time will it pass a tunnel 230 m long ?

Soln. Speed of  the train  =  u  =   m/sec.  =  20 m/sec.

And  x  =  170  m,  z  =  230 m.

∴  Time taken to pass a tunnel

= 

=   sec   =   20  sec.

(17) A train 500 m long is running with a speed of  100 kmph. In what time will it pass a man who is running at 10 kmph in the same direction in which the train in going ?

Soln. The speed of  the train = u = 100 kmph   &   the speed of  a man = v = 10 kmph.

∴   u – v  =  90 kmph  =  90 × m / sec.  =  25  m / sec.,

x  =  500  m.  &  y  =  length of  a man  =  0 m.

∴ Time taken to cross a running man

( Same Direction ) = 

=      sec

=   20  sec.

(18) A train 300 m long is running with a speed of  60 kmph. In what time will it pass a man who is running at 12 kmph in the direction opposite to that in which the train is going ?

Soln. The speed of  the train = u = 60 kmph   &   the speed of  a man = v = 12 kmph.

∴  u + v  =  72 kmph  =  72    m / sec.  =  20  m / sec.,

x  =  300  m.  &  y  =  length of  a man  =  0 m.

∴ Time taken to cross a running man

( Opposite Direction ) = 

=      sec

=   15  sec.

(19) A train 300 meters long takes 10 seconds to cross a man walking at the rate of  4 kmph in a direction opposite to that of  the train. Find the speed of  the train.

Soln. The speed of  the train = u  kmph   &   the speed of  a man = v = 4 kmph.

∴   u + v  =  ( u + 4 )  kmph  =  ( u + 4 ) ×  m / sec.

x  =  300  m.,   y  =  length of  a man  =  0 m.  &  time  =  10 sec.  =   sec.

∴  Time taken to cross a running man

( Opposite Direction ) =

∴      = 

∴    u + 4 = 

=    100

∴   u  =  96  kmph.

i.e.   the speed of  the train is 96 kmph.

(20) Two trains running in the same direction at 70 kmph and 52 kmph completely pass one another in 50 sec. If the length of  the first train is 115m, find the length of  the second train ?

Soln. The speed of  the 1^st  train  =  u  =  70 kmph   &   that of  the 2^nd train  =  v  = 52 kmph.

∴    u – v  =  18 kmph  =  18  m / sec.  =  5  m / sec.,

x  =  115  m.  &  y  =  ?

∴  Time taken to cross a running man

( Same Direction ) = 

∴   50  = 

∴   y  =  135  m.

Thus,  the length of  the 2^nd train = 135 m.

Click here to see more examples