Question

# Places $$A$$ and $$B$$ are $$100 km$$ apart on a highway. One car starts from $$A$$ and another from $$B$$ at the same time. If the cars travel in the same direction at different speeds, they meet in $$5$$ hours. If they travel towards each other, they meet in $$1$$ hour. What are the speeds of the two cars

Solution

## When 2 bodies travel towards each other, the relative velocity is the sum of two and when 2 bodies travel in the same direction, the relative velocity is the difference of two.let velocity of a car starting from $$A=a Km/hr$$and velocity of a car starting from $$B=b Km/hr$$So,when they move towards each other,relative velocity$$=a+b$$when they move in the same direction,relative velocity$$=a-b$$$$velocity=\dfrac{Distance}{Time}$$So,$$a+b=\dfrac{100}{1}$$ and $$a-b=\dfrac{100}{5}$$$$a+b=100$$   and $$a-b=20$$adding two equation,$$2a=120$$$$a=60 Km/hr$$and $$b=100-60$$$$=40 Km/hr$$Thus , speed a two cars will be $$60Km/hr$$ and $$40Km/hr$$Physics

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