SOLUTION: A ride at an amusement park consists of two circular rings of swings. At full speed the swings in the inner ring travel on a circular path with a radius of 32 feet and the swings i

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Question 768502: A ride at an amusement park consists of two circular rings of swings. At full speed the swings in the inner ring travel on a circular path with a radius of 32 feet and the swings in the outer ring travel on a circular path with a radius of 38 feet. Each swing makes one complete revolution every 3.25 seconds. How much greater, in miles per hour, is the linear speed of the swings in the outer ring than the linear speed of the swings in the inner ring? Round to the nearest tenth.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THe circumference of a circle with radius r can be calculated as 2pi%2Ar.
The inner circular path has a length (circumference) of
2pi%2832feet%29= approx. 201.0619feet.
The outer circular path has a length (circumference) of
2pi%2838feet%29= approx. 238.7610feet
The difference in length is 238.7610feet-201.0619feet=37.6991feet.
Converting into miles:
37.6991feet%281mile%2F5280feet%29=37.6991%2F5280miles
That is the difference in distance traveled by the outer ring of seats over the inner ring of seats as the rides goes through one turn in 3.25 seconds.
Converting into hours:
3.25seconds%281hour%2F60minutes%29%281+minute%2F60seconds%29=3.25%2F3660hours
The difference in linear velocities is
%2837.6991%2F5280%29miles divided by %283.25%2F3660%29hours
miles%2Fhour=8.04%29 miles per hour
miles per hour (rounded to the nearest tenth).
Rounded to the nearest tenth, the linear speed of the swings in the outer ring is highlight%28%228.0%22%29 miles per hour greater than the linear speed of the swings in the inner ring.