Question

Places $A$ and $B$ are $100km$ 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

Answer 1

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 $A=aKm/hr$

and velocity of a car starting from $B=bKm/hr$

So,

when they move towards each other,

relative velocity$=a+b$

when they move in the same direction,

relative velocity$=a-b$

$velocity=\frac{Distance}{Time}$

So,

$a+b=\frac{100}{1}$ and $a-b=\frac{100}{5}$

$a+b=100$ and $a-b=20$

adding two equation,

$2a=120$

$a=60Km/hr$

and $b=100-60$

$=40Km/hr$

Thus , speed a two cars will be $60Km/hr$ and $40Km/hr$