Raja’s office is 9 km from his home. One day, he decided to jog to work in order to increase his fitness. He estimates the journey time to be a little over 1 hour 45 minutes.
At first he feels fine, but before long his energy beings to fade and he realizes he will not be able to run the whole distance. A passing taxi is the answer to his prayer. Raja hails the cab and completes his journey, arriving at work one hour 10 minutes earlier than he had anticipated.
Assuming Raja could at 1/6 the speed of the cab, how far did he run before he hailed the taxi?