An athlete runs $5000 \mathrm{~m}$ per week on a sports field, which has a short track and a long track. In a certain week, he trained six days, each day running once on the long track and twice on the short track. In the following week, he trained seven days, each day running once on each track. We can then state that:

(a) the long track is $500 \mathrm{~m}$ longer than the short one;

(b) the long track is four times longer than the short one;

(c) the long track is five times longer than the short one;

(d) the long track is $600 \mathrm{~m}$ longer than the short one;

(e) the long track is three times longer than the short one.
The correct option is (c).

Solution 1: Let's denote by $x$ and $y$ the lengths of the long and short tracks, respectively. In a certain week, the athlete runs $6(x+2 y)$ and, in the other week, $7(x+y)$. Since in both weeks he runs the same 5000 meters, we get $6(x+2 y)=7(x+y)$. Therefore, $6 x+12 y=7 x+7 y$ and, thus, $5 y=x$. Hence, the long track is five times longer than the short track.

Solution 2: In the week when the athlete trained for seven days, he ran one more long track and five fewer short tracks than in the week when he trained only six days. Since the distance run was the same in both weeks, we conclude that the length of the long track is equal to the length of five short tracks.