Question
A thief is spotted by a policeman from a distance of 108
m. The thief starts running and the policeman chases him. If the speed of the thief and policeman are 21 km/h and 23 km/h, respectively, then how far will the thief have to run (in m) before he is overtaken by the policeman?Solution
Distance between policeman and thief = 108 m. Since the speed of the thief is 21 km/hr. and, That of the policeman is 23 km/hr. Relative speed = 21-23 = 2 km/hr. = 2 x (5/18) = 5/9 m/s=0.555 m/sec =0.56 m/sec Time is taken by police to overtake the thief 108/ (5/9) = 972/0.56=192.8sec Hence, the thief will be caught after 192.8sec. Therefore, the distance travelled by the thief before overtaken. = Speed of thief x time taken by a thief = 21 x (5/18) × 192.8 = 1124.6m
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