problems on trains
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Speed of train relative to jogger = (45  9) km/hr = 36 km/hr.
=  36 x  5  m/sec  
18 
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.
Time taken =  360  sec  = 36 sec.  
10 
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Relative speed = (120 + 80) km/hr
=  200 x  5  m/sec  
18 
=  500  m/sec.  
9 
Let the length of the other train be x metres.
Then,  x + 270  =  500 
9  9 
x + 270 = 500
x = 230.
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Speed =  72 x  5  m/sec  = 20 m/sec.  
18 
Time = 26 sec.
Let the length of the train be x metres.
Then,  x + 250  = 20 
26 
x + 250 = 520
x = 270.
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
(100 + 100)  = 3x  
8 
24x = 200
x =  25  . 
3 
So, speed of the faster train =  50  m/sec 
3 
=  50  x  18  km/hr  
3  5 
= 60 km/hr.
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Relative speed = (60 + 40) km/hr =  100 x  5  m/sec  =  250  m/sec.  
18  9 
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time =  300 x  9  sec  =  54  sec = 10.8 sec.  
250  5 
A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
=  66 x  5  m/sec  
18 
=  55  m/sec.  
3 
Time taken to pass the man =  110 x  3  sec = 6 sec.  
55 
A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
Total distance covered 



Time taken 






= 3 min. 
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
Speed =  78 x  5  m/sec  =  65  m/sec.  
18  3 
Time = 1 minute = 60 seconds.
Let the length of the tunnel be x metres.
Then,  800 + x  =  65  
60  3 
3(800 + x) = 3900
x = 500.
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Speed =  300  m/sec =  50  m/sec.  
18  3 
Let the length of the platform be x metres.
Then,  x + 300  =  50  
39  3 
3(x + 300) = 1950
x = 350 m.
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Let the length of the train be x metres and its speed by y m/sec.
Then,  x  = 15 y =  x  . 
y  15 
x + 100  =  x  
25  15 
15(x + 100) = 25x
15x + 1500 = 25x
1500 = 10x
x = 150 m.