Question

Points $A$ and $B$ are $70km$. apart on 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 one hour. Find the speed of the two cars.

Answer 1

Let the speed of the car at point A be $x$ and speed of the car at point B be $y$

W,e know that

$Distance=speed\times time$

Considering the first condition:

When cars were in the same direction,

$Speed=x-y$

$\Rightarrow 70=7(x-y)$

$\Rightarrow x-y=10$--------(1)

Considering the first condition:

When cars were in the opposite direction,

$Speed=x+y$

$\Rightarrow 70=1(x+y)$

$\Rightarrow x+y=70$--------(2)

Solving eq 1 and 2 we have,

$x-y=10$

$x+y=70$

___________

$2x=80$

$\therefore x=40$

and $y=70-40$ from eq 2

So, the speed of the car at the point A $40$ km/hr and speed of the car at the point B is $30$ km/hr