A robber is in a fast car, hurrying away from the scene of his crime. His car can go at 150 km/h. He will be safe if he can reach the border, 40km away. A police car arrives at the scene of the crime. The police are late! The robber has already travelled 10 km towards the border. The police car set off in hot pursuit. Question: calculate how long it will take the robber to reach the border.
Question 2: How fast must the police car travel if it is to catch the robber before he reaches the border ?
Answers
The time taken for a robber to reach the border is 0.2 hours.
The speed of the police car to catch the robber before he reaches the border should be greater than 200 km/hr.
Given:
Let v1,d1, and t1 be the velocity, distance, and time taken for a robber.
v1 = 150 km/hr
The robber has already traveled 10 km
∵ d1 = 40-10 = 30 km
To Find:
The time is taken for a robber to reach the border.
The speed of the police car to catch the robber before he reaches the border.
Solution:
1) we know, v = d/t
t = d/v
= 30/150
= 0.2 hr
Therefore, The time taken for a robber to reach the border is 0.2 hours.
2) To find the speed of the police car to catch the robber before he reaches the border
d = 40 km (∵ as the police start chasing now)
t = 1/5 hr
v > d/t
> 40/0.2
> 200 km/hr
Therefore, The speed of the police car to catch the robber before he reaches the border should be greater than 200 km/hr.
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