9. Police and thief

A thief runs at a constant speed of 210 metres per minute. After one minute, a police officer chases down the robber to catch him. He starts at a speed of 210\(m/minute\), and gradually increases his speed by 10\(m/minute\) every minute after that. How long will it take the cop to catch the thief?

 

 

The Policeman takes 810117 minutes to catch the thief.