Question

The distance between the two towns is $300km$. Car $A$ and Car $B$ start simultaneously from these towns and move towards each other. The speed of Car $A$ is more than that of Car $B$ by $7km/h$. If the distance between the cars after two hours is $34km$. Find the speed of both cars.

• A. Speed of car $B$ is $63$ km/h and speed of car $A$ is $70$ km/h
• B. Speed of car $B$ is $70$ km/h and speed of car $A$ is $75$ km/h
• C. Speed of car $B$ is $50$ km/h and speed of car $A$ is $65$ km/h
• D. Speed of car $B$ is $72$ km/h and speed of car $A$ is $80$ km/h

Answer 1

The correct option is A Speed of car $B$ is $63km/h$ and speed of car $A$ is $70km/h$

Let the speed of car $B$ be $xkm/h$
Then, speed of car $A=(x+7)km/h$

Now, distance covered by car $B$ in $2$ hours$=2xkm$ and
Distance covered by car $A$ in $2$ hours $=2(x+7)km$
Given, distance between the cars after two hours is $34km$ and distance between both the towns is $300km$.
So, distance covered by both the cars in two hours moving in the opposite direction
$=300-34=266$ km
According to the question,
Distance covered by car $A+$ Distance covered by car $B=266$
$\Rightarrow 2x+2(x+7)=266$

$\Rightarrow 2x+2x+14=266$

$\Rightarrow 4x+14=266$
$\Rightarrow 4x=266-14$
$\Rightarrow 4x=252$
$\Rightarrow \frac{4x}{4}=\frac{252}{4}$

$\Rightarrow x=63km/h$

Therefore, speed of car $B=63km/h$ and speed of car $A=63+7=70km/h$.