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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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