Motor-cyclist P started his journey at a speed of 30 km/hr. After 30 minutes, motor cyclist Q started from the same place but with the speed of 40 km/hr. How much time will Q take to overtake P?

Motor-cyclist P started his journey at a speed of 30 km/hr. After 30 minutes, motor cyclist Q started from the same place but with a speed of 40 km/hr. How much time will Q take to overtake P?
[A]$latex 1\ hours$
[B]$latex \frac{3}{8}\ hours&s=1$
[C]$latex \frac{3}{2}\ hours&s=1$
[D]$latex 2\ hours$

$latex \mathbf{\frac{3}{2}\ hours}&s=1$
Distance covered by motor cyclist P in 30 minutes.
$latex = 30\times \frac{1}{2} = 15\ km&s=1$
Relative Speed = 40 – 30 = 10 km/hr
∴ Required Speed = Time taken to cover is km at 10 km/hr
$latex = \frac{15}{10} = \frac{3}{2}\ hours&s=1$
Hence option [C] is correct answer.


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