The tires located on the front of the car wears out after $25000$ km, while the tires on the back wears out after $15000$ km. How far can you maximum ride with new tires if you can swap the tires during the journey?
2026-04-07 12:03:47.1775563427
Problem solving: How far is the maximum distance?
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Clearly each pair of tires will spend the same distance $d$ front and rear. During the time they are on the front, they will use up $\frac d{25000}$ of their life. On the rear, they will use up $\frac d{15000}$ of their life, so $\frac d{25000}+\frac d{15000}=1$