# trigonometry application : tire durability

Two new cars are each driven at an average speed of 60 mph for an extended highway test drive of 2000 miles. The diameter of the wheels of the two cars are 15 in. and 16 in., respectively. If the cars use tires of equal durability and profile, differing only by the diameter, which car will probably need new tires first.

How do I answer this kind of problem? Shall I use linear velocity? In what way can I provide a better explanation that the smaller tire will need new tires? It's just a hypothesis I made since if the tire is smaller, it will surely wear off than that of the bigger tire because it will rotate faster than that of the bigger one. So the surface of the smaller tire is used more than that of the bigger tire. I don't know how to explain mathematically. Please help.

The number of revolutions of the wheels is given by: $N=\dfrac{L}{\pi d}$ where $d$ is the diameter and $L$ is the path length. No trigonometry is needed andyour intition is correct.
If $N_0$ is the the number of revolutions after wich we must change the wheelers, than, from the velocity you can find the time as $t_0=\dfrac{N_0 \pi d}{v}$.