Relative Speed and distance formulas with example

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Definition: Speed of one object with respect to another is called relative speed. 

1. If two objects move in same direction at different speeds

If speed of 1st object = x km/hr and
Speed of 2nd object = y km/hr

Therefore, their relative speed = (x – y) km/hr [x > y]

2. Time after which the two objects meet = distance / relative speed = d km/ (x – y) km/hr

3. Distance covered in ‘t’ hours = time × relative speed = t hours × (x – y) km/hr

Let's apply above formula and solve the below example 

Example  : A walks at a speed of 4 kmph and 4 hours after his start , B cycles after him at 10 kmph. How far from the start does B Catch up with A ?
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Solution: A is travelling with a speed of 4 kmph . So in 4 hours A travels a distance = (4 X 4)

=16 km (Distance=Speed X Time)

Then B travels to start at 10 kmph. So 

Relative speed of A and B is = (10- 4)= 6 kmph {According to Formula 1 }

Now according to formula 2, they will meet at a time t=16/6=2.67 hrs.

Which means B has to travel at 10 kmph for 2.67 kms in order to meet A

i.e Total distance B has to cover from starting point is = 10X2.67=26.7 kms

So B will catch up A at 26.7kms from starting point.

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