Question

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

Answer 1

Let the speeds of the cars be $x$ km/hr and $y$ km/hr

Case $1:$ When the cars are going in the same direction

Relative speed $=x-y$

Distance $=100$ km

Time $=\frac{100}{(x-y)}=5$ hrs

$\therefore x–y=20$ ..........(1)

Case $2:$ When the cars are going in the opposite direction

Relative speed $=x+y$

Time $=\frac{100}{(x+y)}=1$ hrs

$\therefore x+y=100$ ..........(2)

Solving the equations (1) and (2) we get,

$x=60,y=40$

Hence, the speeds of the cars are $60$ km/hr and $40$ km/hr.