## Introduction- Problems on trains

Problems on trains are simply a part of time and distance chapter frequently asked in many exams.Let’s play with the problems based on train. Train is simply a safer, faster and cheaper mode of transportation. We all have travelled through many trains. A common scenario of crossing a train is observed while sitting on a station bench or window seat.

#### Case 1

When a train passes a human or pole which has no length, the distance travelled to cross the human or pole will be equal to the length of the train.

##### Question

Ramu is waiting for a train.A train of 50 m passes him at the speed of 36 km/hr. what is the total time taken by the train to cross him?

**Answer-** Total distance travelled by the train while crossing Ramu = Distance between train head and train tail = Length of train

D = 50 m

V= 36 km/hr = 10 m/sec

T= (D/V)= 5 sec

#### Case 2

When a train passes an object with certain length ( O ) , the distance travelled will not be equal to the length of train in this case.

Distance travelled = Length of train + Length of object

##### Question

Ramu is waiting for a train of 50 meter on a platform of 80 meter. A train passes the platform at the speed of 36 km/hr . Find the time taken to cross the platform.

**Answer** Total distance travelled = Length of the train + Length of the platform

D = 50+80 = 130 m

V = 36 km/hr = 10 m/sec

Time taken, T = 130/10 = 13 sec

#### Case 3

The new case arises when a train passes a moving object eg. car,train,trolly etc.In this situation we use the concept of relative velocity.When the speed is expressed with the respect of a moving object , it is called relative velocity.

A. when two trains are moving in the same direction with speed S1 and S2 .Relative speed = S1 – S2 (S1>S2)

B.When two trains are approaching each other ,Relative speed = S1+S2

##### Question

Two trains of length 50 m and 25 m are approaching each other at the speed of 36 km/hr and 54 km/hr.find the time taken to cross each other.

**Answer**

Since, trains are approaching so relative speed = 10 m/sec + 15 m/sec = 25 m/sec

Total Distance = 50 m +25 m = 75 m

So time taken = (D/S) = 3 sec

**Note-** The same question can be asked given trains are moving in the same direction.Relative speed will be the difference of two speeds.

Relative Speed = 15 m/sec – 10 m/sec = 5 m/sec

Time taken = (D/S) = (75/5) = 15 sec

### Summary of Problems on trains

St=Speed of the train , So=Speed of object , Lt=Length of train , Lo =Length of the object

t= time

**Case 1** Train crossing a stationary object without length

St * t= Lt

**Case 2** Train crossing an object with length

St * t = Lt+Lo

**Case 3** Train cossing a moving object without length

In opposite direction (St+So) * t = Lt

In same direction (St-So) * t = Lt

**Case 4 **Train crossing a moving object with length

In opposite direction (St+So) * t =Lt + Lo

In same direction (St-So) * t = Lt +Lo

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