Final answer:
To find out how much farther a runner on the outside edge of the track goes than a runner on the inside edge when they each complete one lap, we calculate the difference in distances covered by the two runners. The inside edge of the track corresponds to the dimensions of the rectangle, while the outside edge includes the dimensions of the rectangle and the semicircles at each end. The length of the outside edge is approximately 226.08 meters longer than the length of the inside edge.
Step-by-step explanation:
To find out how much farther a runner on the outside edge of the track goes than a runner on the inside edge when they each complete one lap, we need to calculate the difference in distances covered by the two runners. The inside edge of the track corresponds to the dimensions of the rectangle, while the outside edge includes the dimensions of the rectangle and the semicircles at each end.
The length of the inside edge of the track is 85 meters, while the length of the outside edge is 85 meters plus two times the circumference of a semicircle with a radius of 36 meters (since the track is 10 meters wide). The formula to calculate the circumference of a circle is C = 2πr, where r is the radius of the circle. So the circumference of each semicircle is C = π × 36 meters. Therefore, the length of the outside edge is 85 meters + 2 × π × 36 meters.
Using the approximation of π as 3.14, the length of the outside edge of the track is approximately 85 meters + 2 × 3.14 × 36 meters = 85 meters + 226.08 meters = 311.08 meters.
The difference in distances covered by the two runners is the length of the outside edge minus the length of the inside edge, which is 311.08 meters - 85 meters = 226.08 meters.
Therefore, a runner on the outside edge of the track will go approximately 226.08 meters farther than a runner on the inside edge when they each complete one lap.