6. (15 points) Every day, Ivan Ivanovich is taken to work by a company car. One day, Ivan Ivanovich decided to walk and left the house an hour earlier than usual. On the way, he met the company car and finished the journey in it. As a result, he arrived at work 10 minutes earlier than the usual time. How long did Ivan Ivanovich walk?
Answer: 55 minutes.

Solution. Since Ivan Ivanovich saved the driver 10 minutes by walking, the car travels from Ivan Ivanovich's house to the meeting point in 5 minutes.

We get: $u T=5 v$,

(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: $s=u T+v(t-T+50)$.

Solving the system of equations (1), (2), and (3), we get: $T=55$ minutes.