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Speed of car is 90% of cruiser.

Source:

February 19, 2011
ratioabsolute value

Problem Statement

From a police station situated on a straight road in nite in both directions, a thief has stolen a police car. Its maximal speed equals 9090% of the maximal speed of a police cruiser. When the theft is discovered some time later, a policeman starts to pursue the thief on a cruiser. However, he does not know in which direction along the road the thief has gone, nor does he know how long ago the car has been stolen. Is it possible for the policeman to catch the thief?