Final answer:
Mai travels 6 * π feet farther than Kiran in one rotation of the carousel. Mai travels 3 * π / 2 feet per second faster than Kiran.
Step-by-step explanation:
To find out how much farther Mai travels than Kiran in one rotation of the carousel, we need to compare the distances they travel. The distance traveled by an object moving in a circle is equal to the circumference of the circle. So, the distance Kiran travels is equal to the circumference of the inner ring, while the distance Mai travels is equal to the circumference of the outer ring.
The circumference of a circle can be calculated using the formula: circumference = 2 * π * radius. Therefore, the distance Kiran travels is 2 * π * 9 feet, while the distance Mai travels is 2 * π * 12 feet.
Subtracting the distance Kiran travels from the distance Mai travels will give us the difference in their distances. So, Mai travels 2 * π * 12 - 2 * π * 9 = 6 * π feet farther than Kiran in one rotation of the carousel.
To find out how much faster Mai travels than Kiran in feet per second, we need to find their respective speeds. The speed of an object moving in a circle is equal to the distance traveled divided by the time taken.
The time taken for one rotation of the carousel is given as 12 seconds. Therefore, Kiran's speed is 2 * π * 9 / 12 feet per second, and Mai's speed is 2 * π * 12 / 12 feet per second.
Subtracting Kiran's speed from Mai's speed will give us the difference in their speeds. So, Mai travels (2 * π * 12 / 12) - (2 * π * 9 / 12) = 3 * π / 2 feet per second faster than Kiran.