Question

Points A and B are 70 km apart on a highway. One car start from A and the another one from B at the same time. If they travel in the same direction, they meet in 7 hours. But if they travel towards each other, they meet in one hour. The speeds of the two cars are

• A. $45$ km/hr and $25$ km/hr
• B. $70$ km/hr and $10$ km/hr
• C. $40$ km/hr and $30$ km/hr
• D. $60$ km/hr and $40$ km/hr

Answer 1

The correct option is C $40$ km/hr and $30$ km/hr

Let speed of the car at A $=$ a km/hr
and speed of the car at B $=$ b km/hr.
If both the cars run in the same direction, then relative motion of the car at A w.r.t. the car at B $=(a-b)$ km/h,
If both the cars run in the opposite direction, then relative motion of the car at A w.r.t. the car at B $=(a+b)$ km/h,
$\therefore 7(a-b)=a+b$
$\Rightarrow 6a=8b$
$\Rightarrow \frac{a}{b}=\frac{4}{3}$
$\therefore$ Speed of the car at A $=70\times \frac{4}{4+3}=40$ km/hr
and speed of the car at B$=70\times \frac{3}{4+3}=30$ km/hr.