SOLUTION: Runners running on a curved track starting point are staggered. This is so each runner runs the same distance to the finish line. If the radius of the inside is x and each lane is

Algebra ->  Expressions-with-variables -> SOLUTION: Runners running on a curved track starting point are staggered. This is so each runner runs the same distance to the finish line. If the radius of the inside is x and each lane is      Log On


   

Question 936492: Runners running on a curved track starting point are staggered. This is so each runner runs the same distance to the finish line. If the radius of the inside is x and each lane is 2.5 feet wide, how far apart should the officials start the runners in the two inside lanes?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's look at the distance once around.
For the inside radius, x, the circumference would be,
C%5Bx%5D=2pi%2Ax
For the next lane at radius, x+2.5, the circumference would be,
C=2pi%2A%28x%2B2.5%29=2pix%2B5pi=C%5Bx%5D%2B5pi
So the next lane would run an additional 5 pi to get to the same point.
So if you stagger the inside runner back 5pi feet, they would run the same distance.
So every lane would be staggered 5pi feet from the lanes around it, clockwise going inwards, counterclockwise going outwards (assuming the race is counterclockwise).