6. (15 points) Every day, Ivan Ivanovich is taken to work by a company car. One day, Ivan Ivanovich decided to walk and left home one and a half hours earlier than usual. On the way, he met the company car and finished the journey in it. As a result, he arrived at work 20 minutes earlier than the usual time. How long did Ivan Ivanovich walk?
Answer: 80 minutes.

Solution. Since Ivan Ivanovich saved the driver 20 minutes by walking, the car takes 10 minutes to drive from Ivan Ivanovich's house to the meeting point.

We get: $u T=10 v$,

(2 points)

where $u$ is Ivan Ivanovich's walking speed, $v$ is the car's speed, and $T$ is the time Ivan Ivanovich walked. The distance from Ivan Ivanovich's house to his workplace: $s=v t$,

and on the other hand: $s=u T+v(t-T+70)$.

(4 points)

Solving the system of equations (1), (2), and (3), we get $T=80$ minutes.

(4 points)