A thief stole jewellery from a shop at 8:15 p.m. and left on a bike at a speed of 60 km/h. The police were informed at 8:30 p.m. If the police want to arrest the thief at 9:00 p.m., what should be the minimum speed of the police jeep?

Given:

Time when the thief stole the jewellery = 8:15 p.m.

Speed of thief's bike = 60 km/h

Time when police were informed = 8:30 p.m.

Formula used:

Minimum speed of police officer = \(\text {Distance between the thief and the police} \over \text{Time taken by police to reach the thief}\)

Calculation:

If the thief left at 8:15 p.m. and the police wants to catch him at 9:00 p.m., the time for which the thief was on the bike = 45 minutes = \(3 \over 4\) hours = 0.75 hours

Distance travelled by the thief = 60 km/h × 0.75 h = 45 km 

Time taken by the police to reach the thief = 30 minutes = 0.5 hours

Thus, minimum speed of the police jeep should be = \(45\: \text{km} \over 0.5 \:\text{h}\) = (45 × 2) km/h = 90 km/h 

∴ The minimum speed of the police jeep should be 90 km/h.