Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours. But,if they travel towards each other, they meet in 1 hour. Find the speed of the each car.

Let the speed of the car starting from A be $xkm/hr$ and that from B be $ykm/hr$

If they are travelling in opposite direction ie towards each other then effective speed will be $(x+y)km/hr$

If they are travelling in same direction then effective speed will be $(x-y)km/hr$

According to the question,

$\Rightarrow \frac{70}{x-y}=7$...(i) and $\frac{70}{x+y}=1$...(ii)

From (i) and (ii), we get,

$\Rightarrow x-y=10$...(iii) and $x+y=70$...(iv)

Adding (iii) and (iv),

$\Rightarrow 2x=80$

$\therefore x=40km/hr$

Hence, $y=70-40=30km/hr$