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?

Let the speed of first car at $A$ be $xkmph$

and the speed of car at $B$ be $ykmph$

when the cars travel in same direction Relative Speed is $S=x-y$

Distance$D=100km$

Time, $t=5$ hours

Since, Speed$=\frac{\text{Distance}\left(D\right)}{\text{Time}\left(T\right)}$

$\therefore$ Distance $D=S\times T$

Substitute given values, we get

$\Rightarrow 100=(x-y)\times 5$

$\therefore x-y=20$.......(i)

when cars travel in opposite direction Relative Speed is $x+y$

Distance$=100km$

$t=1$ hours

Distance $D=ST$

$\Rightarrow 100=(x+y)$

$x+y=100$.......(ii)

Adding equations (i) & (ii), we get

$x-y+x+y=20+100$

$\Rightarrow 2x=120$

$\therefore x=60km/h$

From equation(i), $y=60-20$

$\therefore y=40km/h$

Hence, Speed of the car at $A=60km/h$ and

Speed of the car at $B=40km/h$