Question

Two stations A and B are $90$ km apart and on a highway. A car starts from A and another from B at the same time. If they go in the same direction, they meet after $9$ hours and if they go in opposite directions, they meet after $1\frac{2}{7}$ hours. Find the speeds of both the cars.

• A. Speed of Car A $=13km/hr$ and speed of Car B $=20km/hr$
• B. Speed of Car A $=55km/hr$ and speed of Car B $=40km/hr$
• C. Speed of Car A $=40km/hr$ and speed of Car B $=30km/hr$
• D. Speed of Car A $=10km/hr$ and speed of Car B $=22km/hr$

Answer 1

Answer: (C)

Speed of Car A $=40km/hr$ and speed of Car B $=30km/hr$

When they travel in same direction, suppose they meet when B travels for $x$ m, then A will have travelled $(90+x)$m in the same time.

Since, Speed $=\frac{Distance}{Time}$
$\therefore \text{Speed of car at A}=\frac{x+90}{9}$

And Speed of car at B $=\frac{x}{9}$
When they travel in the opposite direction, suppose they meet when A travels for $y$ m, then B will have travelled $90-y$ m in the same time

$1\frac{2}{7}$ hours $=\frac{9}{7}$ hour

Speed of car at A $=\frac{y}{\frac{9}{7}}=\frac{7y}{9}$

And Speed of car at B $=\frac{90-y}{\frac{9}{7}}=\frac{7(90-y)}{9}$

Equating the speeds of the cars in both the cases,
Speed of car at A, $\frac{x+90}{9}=\frac{7y}{9}$
$x+90=7y$
$=>x-7y=-90$ --- (1)
Speed of car at B, $\frac{x}{9}=\frac{7(90-y)}{9}$
$=>x+7y=630$ --- (2)
Adding equations $1$ and $2$, we get $2x=540=>x=270$

So, Speed of car at A $=\frac{x+90}{9}=\frac{360}{9}=40km/hr$
Speed of car at B $=\frac{x}{9}=\frac{270}{9}=30km/hr$