A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 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 = 100 metres/minute
∴ Distance covered by thief in (t + 1) minutes = 100 metres/minute × (t + 1) minutes = 100 (t + 1) metres
Distance covered by policeman in t minutes = Sum of t terms of an AP with first term 100 and common difference 10
When the policeman catches the thief,
⇒ t = − 4 and t = 5
∴ t = 5 (As t cannot be negative)
Thus, the policeman catches the thief after 5 minutes.