Yeesh. This thread points out how dismal the math skills of the average person in this country really are. You guys are college students, right? Some have already explained this, but for those still confused, allow me to try a different approach:
All you care about is the length difference between two concentric lanes, right? In other words, you want length_outer - length_inner. Let's call them L1 for outer and L2 for inner (diff=L1-L2). What's the length of any lane on the curve? For one revolution, it's pi*diameter. So, if we call the diameter of the outer lane D1, and for the inner, D2, then then we have:
L1=pi*D1 and L2=pi*D2,
thus
L1-L2 = pi*D1 - pi*D2 or,
L1-L2 = pi(D1-D2)
as L1-L2 = length difference, then
len diff = pi(D1-D2)
When you measure from one lane to another, you are measuring the difference from the origin, or the radius. As the diameter is twice the radius, we have:
len diff = 2*pi*diff_between_lanes
So, if you had 4 foot wide lanes and you're running in lane 8, you're 7 lanes or 28 feet over from lane 1. Thus you're running 2*pi*28' = 176' or 53.6 meters more per lap. As you can see, it doesn't matter how long the straights are. For that matter, the "turns" could be cut in half again so that you have 4 straights per lap and it works out the same.
Hope this helps.