Question 438802: Sami has a 10 speed bike. the radius of the large sprocket attached to the pedal is 4 inches. In 7th gear, the radius of the sprocket attached to the back wheel is 1.5 inches. When sami makes the pedal go 1 revolution, the bike travels 100 feet. What is the radius of the wheel of Sami's bike?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Sami has a 10 speed bike. the radius of the large sprocket attached to the pedal is 4 inches. In 7th gear, the radius of the sprocket attached to the back wheel is 1.5 inches. When sami makes the pedal go 1 revolution, the bike travels 100 feet. What is the radius of the wheel of Sami's bike?
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Circumference of a circle = (pi)d where d is the diameter.
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Circumference of large sprocket = 8(pi) inches
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Circum of small sprocket = 3(pi)
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When large moves 1 revolution small moves 8/3 revolutions.
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Distance traveled per revolution = 100ft/(8/3) = 300/8 = 37.5 ft
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Circumference of wheel on Sami's bike = 37.5ft
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C = (pi)(2r)
37.5/(2pi)= r
radius = 5.97 ft.
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Cheers,
Stan H.
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