8.2. On weekdays (from Monday to Friday), Petya worked out in the gym five times. It is known that in total he spent 135 minutes in the gym, and the time spent in the gym on any two different days differed by at least 7 minutes. What is the maximum duration that the shortest workout could have been?
Answer: 13 minutes.

Solution. Let the minimum training time be $x$ minutes, then the second (in terms of duration) is no less than $x+7$, the third is no less than $x+14$, the fourth is no less than $x+21$, and the fifth is no less than $x+28$. Therefore, the total duration of the trainings is no less than $5 x+70$ minutes.

Solving the inequality $135 \geq 5 x+70$, we get $x \leq 13$. A suitable duration for the trainings is 13, 20, 27, 34, and 41 minutes.

Comment. Correct answer without justification - 0 points.

Proved that the shortest session cannot last more than 13 minutes - 5 points. Provided an example - 2 points.