Question

Places $A$ and $B$ are $80km$ apart from each other on a highway. A car starts from $A$ and other from $B$ at the same time. If they move in the same direction they meet in $8$ hours and if they move towards each other they meet in $1$ hour and $20$ minutes. Find the speeds of the cars.

Answer 1

Let the speed of car starting from $A=x$ km/hr and speed of car starting from $B=y$ km/hr.

The relative speed of $A$ with respect to $B$ when moving in the same direction $=x-y$ km/hr.

The relative speed of $A$ with respect to $B$ when moving in opposite direction $=x+y$ km/hr.

Distance between $A$ and $B=80$ km.

We know, $Time=\frac{Distance}{Speed}$

From the above information, we have,

$\frac{80}{x-y}=8and\frac{80}{x+y}=1+\frac{20}{60}=\frac{4}{3}$

$or,\frac{80}{x-y}=8$

$\Rightarrow 10=x-y$

$\Rightarrow x-y=\mathrm{10....}\left(i\right)$

$Also,\frac{80}{x+y}=\frac{4}{3}$

$\Rightarrow 240=4(x+y)$

$\Rightarrow x=60-y....\left(ii\right)$

Substituting (ii) in (i), we get,

$x-y=10$

$\Rightarrow 60-y-y=10$

$\Rightarrow 60-2y=10$

$\Rightarrow 2y=50$

$\Rightarrow y=25$

Substituting $y=25$ in equation (ii), we get,

$x=60-y$

$\Rightarrow x=60-25$

$\Rightarrow x=35$

Thus, the speed of car starting from $A=x=35$ km/hr and speed of car starting from $B=y=25$ km/hr.