Question on radius problem A car with 15 inch radius tires was driven on a trip of a distance equal to 400 miles. Two months later, with snow tires, the odometer indicated 390 miles for the same trip. Find the radius of the snow tires.
This is how I attempted to solve it. 
$2\pi \left( 15 \right)n\; =\; 400\cdot 5280\cdot 12$
Where n is the number of revolutions of the tire, and I converted everything to inches.
You get that n = $\frac{844800}{\pi }$
Then $2\pi \left( r \right)\left( \frac{844800}{\pi } \right)\; =\; 390\cdot 5280\cdot 12$
Solving for r gives $\frac{117}{8}$ inches, but after checking the answer, it seems that it is $\frac{200}{13}$ inches.
Where did I go wrong? I have a feeling it has to do with my approach, as n - the number of revolutions - will not be same for both tires.

Try more symbolics: Let $r_1$ the radius of the tire, $d_1$ the first measured distance, $d_2$ the second measured distance and $r_2$ the radius of the snow tires and $n_1, n_2$ the respective number of revolutions. Then the measurements are
$$2\pi r_1 \cdot n_1 = d_1 = 2\pi r_2 \cdot n_2, 2\pi r_1 \cdot n_2 = d_2$$
so we have
$$n_2 = \frac{d_2}{2\pi r_1} = \frac{d_2}{\frac{d_1}{n_1}} = \frac{d_2 n_1}{d_1}$$
and then
$$r_2 = \frac{d_1}{2\pi n_2} = \frac{d_1}{2\pi \frac{d_2 n_1}{d_1}} = \frac{d_1}{2\pi n_1 \frac{d_2}{d_1}} = \frac{d_1}{\frac{d_1}{r_1}\frac{d_2}{d_1}} = \frac{d_1}{d_2} r_1$$
So finally
$$ r_2 = \frac{400}{390} \cdot 15 = \frac{600}{39} = \frac{200}{13} \text{[in]}$$
