A thief is noticed by a policeman from a distance of 650 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 8 km and 10.5 km per hour, respectively. The distance (in metres) between them after 12 minutes is:
Answer & explanation
Correct answer: option 1
Speed of thief = 8km/h × \(\frac{5}{18}\) = \(\frac{20}{9}\) m/s
Speed of police = 10.5km/h × \(\frac{5}{18}\) = \(\frac{17.5}{6}\) m/s
According to the question,
Distance traveled by thief in 12 mins = \(\frac{20}{9}\) × (12 × 60)
=\(\frac{14400}{9}\)= 1600 m
Distance traveled by police in 12 mins = \(\frac{17.5}{6}\) × (12 × 60)
=2100 m
Distance between thief and police after 12 mins = (Initial distance + distance traveled by a thief in 12 mins) - (Distance traveled by police in 12 mins)
Distance = (650 + 1600) - 2100
= 2250 - 2100 = 150 m
SO , The distance between them after 12 minutes is 150 m.