Two cars $A$ and $B$ are moving with same speed of $45 k m / h r$ along same direction. If a third car $C$ coming from the opposite direction with a speed of $36 k m / h r$ meets two cars in an interval of $5 m i n$ , the distance of separation of two cars $A$ and $B$ should be (in km)

6.75

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7.25

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5.55

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8.35

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Solution

The correct option is A $6.75$
$V_{A} = V_{B} = 45 k m / h r$
$V_{C} = 36 k m / h r$
Let $x$ is the distance between $A$ and $B .$
Velocity of approach between $A$ and $B .$
$\Rightarrow V_{A C} = V_{A} + V_{B} = (45 + 36) k m / h r = 81 k m / h r$
$V_{B C} = V_{B} + V_{C} = (45 + 36) k m / h r = 81 k m / h r$

$\Rightarrow$ Velocity of approach $= \frac{D i s t a n c e b e t w e e n A a n d B}{T i m e d i f f e r e n c e i n m e e t i n g A a n d B}$
$\Rightarrow △ t = 5 m i n = \frac{5}{60}$
$\Rightarrow 81 = \frac{x \times 60}{5}$

$\Rightarrow x = \frac{5 \times 81}{60}$
$= 6.75 k m$
Hence, the answer is $6.75 k m .$

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Two cars A and B are moving with same speed of 45km/hr along same direction. If a third car C coming from the opposite direction with a speed of 36km/hr meets two cars in an interval of 5min, the distance of separation of two cars A and B should be (in km)

Two cars $A$ and $B$ are moving with same speed of $45 k m / h r$ along same direction. If a third car $C$ coming from the opposite direction with a speed of $36 k m / h r$ meets two cars in an interval of $5 m i n$ , the distance of separation of two cars $A$ and $B$ should be (in km)