4. The Carousel on the National Mall in Washington, DC , has 4 rings of horses Andre is riding on the inner ring, which has a radius of 9 ft . Lin is riding on the outer ring, which is 8 ft farther from the center than the inner ring. (a) In one rotation of the carousel, how much farther does Lin travel than Andre

To find out how much farther Lin travels than Andre in one rotation of the carousel, we first need to determine the circumferences of both rings. The formula for the circumference (C) of a circle is given by \( C = 2\pi r \), where \( r \) is the radius. For Andre, riding the inner ring with a radius of 9 ft: \( C_{Andre} = 2\pi(9) = 18\pi \) ft. For Lin, who is on the outer ring which is 8 ft farther from the center, the radius becomes: \( 9 ft + 8 ft = 17 ft \). Thus, Lin's circumference is: \( C_{Lin} = 2\pi(17) = 34\pi \) ft. Now, we calculate the difference in distance traveled: \( C_{Lin} - C_{Andre} = 34\pi - 18\pi = 16\pi \) ft. So in one rotation of the carousel, Lin travels \( 16\pi \) ft farther than Andre. To put that in more relatable terms, that's approximately 50.27 ft (since \( \pi \) is roughly 3.14). Quite the workout for Lin, while Andre enjoys a more leisurely ride! 🎠