Final answer:
Justin can ride his bike approximately 78.5 yards farther on the longer path compared to the shorter path.
Step-by-step explanation:
To find the difference in length between the longer and shorter paths, we first need to find the circumference of each path. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the first path has a diameter of 105 yards, so the radius is half of that, which is 52.5 yards. The circumference of the first path is 2π(52.5) = 105π yards. The second path has a radius of 40 yards, so its circumference is 2π(40) = 80π yards.
To find the difference in length between the two paths, we subtract the circumference of the shorter path from the circumference of the longer path. The difference in length is 105π - 80π = 25π yards. To find an approximate decimal value, we can use the value of π as 3.14. So the difference in length is 25π ≈ 25(3.14) = 78.5 yards. Justin can ride his bike approximately 78.5 yards farther on the longer path compared to the shorter path.