Question

400 m long train crosses a flag post in half a minute. What is its speed?

options:
1) 102 kmph 2) 48 kmph 3) 96 kmph 4) 84 kmph 5) None of these

Answer 1

1.  If two objects are moving in opposite directions towards each other  at speeds u and v, then relative speed = Speed of first + Speed of second = u + v.
This is also the speed at which they are moving towards each other or the speed at which they may be moving away from each other.

2. If the two objects move in the same direction with speeds u and v, then
relative speed = difference of their speeds = u – v. 

This is also the speed at which the faster object is either drawing closer to the slower object or moving away from the slower object as the case may be.

Important Models:

Model 1. 1 Pole and I Train:
Length of The Train (m) = Speed of the Train (m/s) × Time taken to cross the pole (s)

Model 2. 1 Train and 1 Platform: 
Length of the Train + Length of the Platform (m) = Speed of the Train (m/s) × Time taken to cross the platform (s)

Model 3. 1 Train with speed speed v1  and 1 moving person with speed v2
Case 1: If both are moving in same direction
Length of The Train (m) = [Speed of the Train - Speed of the Man] (m/s) × Time taken to cross the man (s)

Case 2: If both are moving in opposite direction
Length of The Train (m) = [Speed of the Train + Speed of the Man] (m/s) × Time taken to cross the man (s)

Model 4. 2 Trains with speeds v1,v2
Case 1: If both are moving in same direction
[Length of The Train 1 + Length of the Train 2](m) = [Speed of the Train1 - Speed of the Train 2] (m/s) × Time taken to cross (s)

Case 2: If both are moving in opposite direction
[Length of The Train 1 + Length of the Train 2](m) = [Speed of the Train1 + Speed of the Train 2] (m/s) × Time taken to cross (s)

Answer 2

speed = distance/time
=400/30 m/s=40/3 m/s
=18/5 × 40/3 km/hr
=48km/hr
option 2 is correct