10.2 A group of friends went for a morning run around a lake. During the run, one by one they realized they had miscalculated their strength, and switched from running to walking. One of the friends calculated that he had run one-eighth of the total distance that the entire group had run, and walked one-tenth of the total distance that they had walked. How many people were on the outing?
Solution 1: Let the person who ran cover $x$ part of the road, then $0<x<1$, and he walked $(1-x)$ part of the way. If there were $n$ people in total, then according to the condition, the total distance covered by the group (expressed in terms of parts) is on one side $n$, and on the other side $8 x + 10(1-x) = 10 - 2 x$. Therefore, $2 x$ is an integer, so the only option is $x=0.5$, and $n=9$.

Solution 2: If this friend ran $a$ km and walked $b$ km, then the total distance covered by the group on one side is $8 a + 10 b$, and on the other side $n(a + b)$. Thus, $n = \frac{8 a + 10 b}{a + b} = 9 + \frac{b - a}{a + b}$. Since $a$ and $b$ are non-zero numbers, the last fraction can only be an integer if $a = b$, otherwise the absolute value of the non-zero numerator will be less than the absolute value of the denominator, and the fraction will not be an integer.

Criteria: The correct equation for the total distance was set up, but no conclusions were drawn, -2 points.