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Answer :
The time that will be taken by the police to catch the robbers is 1 hour and 34.67 minutes.
What is speed?
The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
Speed = Distance Covered / Time taken
Given that police start chasing the robber after 12 minutes. Therefore, the distance covered by robbers in 12 minutes is,
Distance covered by robbers = Speed of robbers × Time
= 71 mph × 12 minutes
= 71 mph × (12/60) hour
= 14.2 miles
Now, since the police and robber both are running at a speed, also, the distance between the two is 14.2 miles. Therefore, the time that will be taken by the police to catch the robbers is,
Time = Distance / Realtive speed
Time = Distance between police and robbers/(Speed of police - Speed of robbers)
Time = 14.2 miles/(80 mph - 71 mph)
Time = 14.2 miles/9mph
Time= 1.5778 hours or 1 hour and 34.67 minutes
Hence, the time that will be taken by the police to catch the robbers is 1 hour and 34.67 minutes.
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