A police officer goes after a thief who has a 120 m headstart. The officer runs 1 km in 5 minutes, and the
thief runs 1 km in 8 minutes. How far could the thief have gone before being overtaken?
Answers
Given : A police officer goes after a thief who has a 120 m headstart.
The officer runs 1 km in 5 minutes, and the thief runs 1 km in 8 minutes.
To Find : How far could the thief have gone before being overtaken
Solution:
Thief had headstart of 120 m
Let say thief has gone d m
thief runs 1 km in 8 minutes
=> 1000 m in 8 minutes
=> 1 m in 8/1000 minutes
=> d m in 8d /1000 minutes
officer runs 1 km in 5 minutes
=> 1000 m in 5 minutes
=> 1 m in 5/1000 minutes
=> d+ 120 m in 5(d + 120)/1000 minutes
Time should be same to catch
5(d + 120)/1000 = 8d /1000
=> 5d + 600 = 8d
=> 3d = 600
=> d = 200
thief have gone 200 m from head start
and 320 m from officer
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