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A horse 64 feet from the center of a merry-go-round makes 27 revolutions. In order to travel the same distance, how many revolutions would a horse 16 feet from the center have to make?

 Jul 20, 2022
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A horse 64 feet from the center of a merry-go-round makes 27 revolutions. In order to travel the same distance, how many revolutions would a horse 16 feet from the center have to make? 

 

The circumference of a circle radius 64 is      2 • π • 64  =  128 π  

The circumference of a circle radius 16 is      2 • π • 16  =    32 π  

 

128 π / 32 π  =  4 

 

So the horse travelling the smaller circle has to go 4 times around to go

the same distance as the horse travelling the larger circle 1 time around. 

 

When the horse travels the distance of 27 times around the outer circle, 

the other horse has to go around 4 times as much for the same distance. 

 

4 • 27  =  108 revolutions  

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 Jul 20, 2022

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