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

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UpStudy AI · Accepted Answer

The radius of the inner ring is $$9$$ ft, so Andre travels a distance of

$$
2\pi(9) = 18\pi \text{ ft}
$$

in one rotation. The outer ring is $$8$$ ft farther from the center, giving it a radius of

$$
9 + 8 = 17 \text{ ft}
$$

Thus, Lin travels

$$
2\pi(17) = 34\pi \text{ ft}
$$

in one rotation. The difference in their distances is

$$
34\pi - 18\pi = 16\pi \text{ ft}
$$
Lin travels $$16\pi$$ feet farther than Andre in one rotation.

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