Answers and Solutions

Answer

Answer:

Let the speed of the first train =  x metres/sec. When a train crosses a pole it travels a distance equal to its own length.The time taken by the train to cross a pole =  5 secs.                                            Therefore length of the first train =  5*x =  5x metres.

When the train crosses a platform it  travels the entire length of the platform and also its own length . The time taken by the train to cross the platform = 15 secs .                                                                                                                        

Therefore the distance traveled by the train =  15*x = 15x.Hence length of the platform=                    

Total distance traveled  - length of the train = 15x -  5x =  10x metres.                                    

Now when two trains cross each other the distance traveled by any one train equals the sum of the lengths of both the trains. Length of the second train =  520 metres

Therefore  total distance traveled by the first train = ( x+520) metres.

Speed of the second train = 44kms/hr =44*1000/3600 =110/9 metres/sec

When two  trains  cross each other,they will cross each other with their relative speed.As both the trains are traveling  in opposite directions,their  relative speed will be sum of the   speed of  individual trains. Therefore relative speed of both the trains = (x+110/9) metres/hr

Time taken to cross each other = Total distance traveled/ Relative speed of the trains= 12

= (5x+520)/{x+(110/9)} =  9(5x+520)/(9x+110) = 12. By cross multiplying we get

9(5x+520) =12(9x+110).Simplifying and solving for x we get x = (1120/21) metres.

Now length of platform = 10x metres. Length of first train = 5x metres. 

Therefore difference between length of the  platform and length of first train = 10x - 5x =5x

=  5*1120/21 = 5600/21 = 800/3 =266.66 metres