Train concept

Problems On Trains 

Problems on trains and Time and Distance are almost same. The only difference is we have to consider the length of the train while solving problems on trains.

Properties of Proplems on Trains

1. Time taken by a train x meters long in passing a signal post or a pole or a standing man = Time taken by the train to cover x meters.

2. Time taken by a train x meters long in passing a stationary object of length y meters = Time taken by the train to cover ( x + y ) metres.

3. Suppose two trains or two bodies are moving in the same direction at u kmph andv kmph such that u > v, then their relative speed = ( u - v ) kmph.

4. If two trains of length x km and y km are moving in the same direction at u kmph and v kmph, where u > v, then time taken by faster train to cross the slower train = { ( x + y ) / ( u - v ) }hrs.

5. Suppose two trains or two bodies are moving in opposite directions at u kmphand v kmph. Then, their relative speed = ( u + v ) kmph.

6. If two trains of length x km and y km are moving in opposite directions at u kmphand v kmph, then: time taken by the trains to cross each other = ( x + y ) / ( u + v ) hrs.

7. If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively. Then, A′s speed : B′s; speed = [ ( 1 / b ) : ( 1 / a ) ].

Basic Formulas

x kmph = [ ( x * ( 5 / 18 ) ] m/sec.

Example sum

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Speed = [ 60 * ( 5 / 18 ) ] m/sec
= ( 50 / 3 ) m/sec
Length of the train = ( Speed * Time )
= [ ( 50 / 3 ) * 9 ] m
= 150 m

Basic Formulas

y m/sec = [ y * ( 18 / 5 ) ] km/hr

Example sum

1.  A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. Find the speed of the train?

Answer: Speed of the train relative to man = ( 125 / 10 ) m/sec
= ( 25 / 2 ) m/sec
= [ ( 25 / 2 ) * ( 18 / 5 ) ] km/hr
= 45 km/hr
Let the speed of the train be x km/hr.
Relative speed = ( x - 5 ) km/hr.
⇒ ( x - 5 ) = 45
⇒ x = 45 + 5
⇒ x = 50 km/hr

Basic Formulas

If two trains of p meters and q meters are moving in same direction at the speed of x m/s and y m/s ( x > y ) respectively then time taken by the faster train to overtake slower train is given by = [ ( p + q ) / ( x - y ) ]

Example sum

1.  Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. Find the length of each train?

Answer: Let the length of each train be x metres.
Distance covered = 2x metres.
Relative speed = ( 46 - 36 ) km/hr
= [ 10 * ( 5 / 18 ) ] m/sec
= ( 25 / 9 ) m/sec
⇒ ( 2x / 36 ) = ( 25 / 9 )
⇒ 2x = 100
x = 50

Basic Formulas

If two trains of p meters and q meters are moving in opposite direction at the speed of x m/s and y m/s respectively then time taken by trains to cross each other is given by = [ ( p + q ) / ( x + y ) ]

Example sum

1. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

Answer: Speed of the first train = ( 120 / 10 ) m/sec
= 12 m/sec
Speed of the second train = ( 120 / 15 ) m/sec
= 8 m/sec
Relative speed = ( 12 + 8 )
= 20 m/sec
Required time = [ ( 120 + 120 ) / 20 ] sec
= 12 sec.