Question

Points A and B are 70 km apart on a highway. A car starts from A and another car starts 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. What are their speeds in km/hr?

• A. $40,20$
• B. $50,30$
• C. $40,30$
• D. None of these

Answer 1

Answer: (C)

$40,30$

When they travel in same direction, suppose
they meet when B travels for $x$ m, then A will have travelled $70+x$
m in the same time
Since, Speed $=\frac{Distance}{Time}$
Speed of car at A $=\frac{x+70}{7}$

And Speed of car at B $=\frac{x}{7}$
And when they travel in the opposite direction, suppose they meet when A
travels for $y$ m, then B will have travelled $70-y$ m in the same
time

Speed of car at A $=\frac{y}{1}=y$

And Speed of car at B $=\frac{70-y}{1}=70-y$

Equating the speeds of the cars in both the cases,
Speed of car at A, $\frac{x+70}{7}=y$
$x+70=7y$
$=>x-7y=-70$ --- (1)
Speed of car at B, $\frac{x}{7}=70-y$
$=>x+7y=490$ --- (2)
Adding equations $1$ and $2$, we get $2x=420=>x=210$
So, Speed of car at A $=\frac{x+70}{7}=\frac{280}{7}=40km/hr$
Speed of car at B $=\frac{x}{7}=\frac{210}{7}=30km/hr$