36. The front tires of a car wear out after 25,000 km, while the rear tires wear out after 15,000 km. When is it advisable to swap the tires to ensure they wear out evenly? (Assume that the tires are swapped once, although drivers do this more frequently in practice.)
36. It is advisable to change the tires so that their wear occurs at the same mileage for all wheels. Let's say they should be changed at $x$ km of mileage, then the front wheels have $(25000-x)$ km left to wear. But if they are put in place of the rear wheels, they can only travel $\frac{15000}{25000}=\frac{3}{5}$ of the distance they would still travel if they remained in their previous position, i.e., $\frac{3}{5}(25000-x)$. The rear wheels will travel $x$ km before the change, and if they remained in their place, they would travel another $(15000-x)$ km. In the position of the front wheels, they would travel $\frac{5}{3}(15000-x)$ km. After the tire change, the wheels should travel the same distance until wear, so $\frac{3}{5}(25000-x)=\frac{5}{3}(15000-x)$, from which $x=9375$ km.