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 31/2 miles long. The train is 1/4 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
= ( 7 + 1 ( miles
2 4
= 15 miles.
4

Therefore Time taken
= ( 15 ( hrs
4 x 75
= 1 hrs
20
= ( 1 x 60 ( min.
20
= 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

Therefore x + 100 = x
25 15

=> 15(x + 100) = 25x

=> 15x + 1500 = 25x

=> 1500 = 10x

=> x = 150 m.