PROBLEMS ON FINDING THE LENGTH OF TRAIN

Time taken by a train of length l meters to pass a pole or standing man or signal post is equal to the time taken by the train to cover l meters.

Time taken by a train of length l meters to pass a standing object of length b meters is the time taken by the train to cover (l + b) meters.

Distance covered by both the trains  =  l + b

If two trains or two bodies are moving in the same direction at u m/s and v m/s, then their

Relative Speed   =  (u  - v)  m / s

Distance covered  =  Sum of length of two trains

Time  =  Sum of length of two trains/Relative speed 

If two trains or two bodies are moving in the opposite direction at u m/s and v m/s, then their

Relative speed  =  (u + v) m/s

then the time taken by the faster train to cross the slower train is 

  =  Sum of length of two trains/Relative speed

To convert minutes into hour, we should divide the given minutes by 60.

  • If you want to convert the speed from km/hr to m/sec, you should multiply the speed by 5/18.
  • If you want to convert the speed from m/sec to km/hr, you should multiply the speed by 18/5.

Examples

Example 1 :

It took a train 50 seconds to pass a tunnel that was 1000 m long. It took the same train, traveling at the same speed, 75 seconds to pass a bridge that was 1625 m long. How long was the train ? At what speed was it travelling ?

Solution :

Let x and l be the speed of the train and length of the train respectively.

Distance covered by the train when it crosses the tunnel of length 1000 m  =  l + 1000

Time taken  =  Distance / Speed

50  =  (l + 1000) / x 

x  =  (l + 1000) / 50  ------(1)

Distance covered by the train when it crosses the bridge of length (l + 1625)

75  =  (l + 1625) / x 

x  =  (l + 1625) / 75 ------(2)

(1)  =  (2)

(l + 1000) / 50  =   (l + 1625) / 75

(l + 1000) / 2  =   (l + 1625) / 3

3(l + 1000)  =  2(l + 1625)

3l + 3000  =  2l + 3250

3l - 2l  =  3250 - 3000

l  =  250 m

By applying the value of l in (1)

x  =  (250 + 1000) / 50

x  =  25 m/sec

To convert the speed from m/sec to km/hr, we get

x  =  25⋅(18/5)

x  =  90 km/hr

Hence the length of the train is 250 m, speed of the train is 50 km/hr.

Example 2 :

Two trains travelled towards each other on different tracks. Train A traveled at a speed of 54 km/hr and Train B travelled at 72 km/hr. A commuter aboard Train A recorded that Train B took 8 seconds to pass his window seat completely. How long was Train B ?

Solution :

Speed of Train A  =  54 km/hr

Speed of Train B   =  72 km/hr

Converting the speed from km/hr to m/sec 

Speed of train A  =  54 ⋅ (5/18)  =   15 m/sec 

Speed of train B  =  72 ⋅ (5/18)  =  20 m/sec

Relative speed  =  15 + 20

  =  35 m/sec

Train B is taking 8 seconds to cross the window seat of train A.

Time  =  Distance covered by Train B / 35

Distance covered by train B  =  Length of train B 

 =  35 ⋅ 8

=  280 m

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