A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?
Suppose the policeman catches the thief after t minutes.
Uniform speed of the thief = 50 m/min
∴ Distance covered by thief in (t + 2) minutes = 50 m/min × (t + 2) min = 50 (t + 2) m
The distance covered by the policeman in t minutes is in AP, with 60 and 5 as the first term and the common difference, respectively.
Distance covered by policeman in t minutes = Sum of t terms
When the policeman catches the thief, we have
So, t = −8 or t = 5
∴ t = 5 (As t cannot be negative)
Thus, the policeman catches the thief after 5 min.