SOLUTION: an antique bike has two wheels. The front wheel has a radius that is 8 times bigger than the smaller wheel in back. when the bike has traveled 100ft the back wheel rotates 60 times

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Question 526049: an antique bike has two wheels. The front wheel has a radius that is 8 times bigger than the smaller wheel in back. when the bike has traveled 100ft the back wheel rotates 60 times more than the larger front wheel. What is the diameter of each wheel?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An antique bike has two wheels.
The front wheel has a radius that is 8 times bigger than the smaller wheel in back.
when the bike has traveled 100ft the back wheel rotates 60 times more than the larger front wheel.
What is the diameter of each wheel?
:
Let d = diameter of the small wheel
then
8d = diameter of the large wheel
:
Change 100 ft to 1200 inches
:
large wheel rotations + 60 = small wheel rotations
1200%2F%28pi%2A8d%29 + 60 = 1200%2F%28pi%2Ad%29
:
Multiply each term by pi%2Ad, results:
1200%2F8 + 60pi%2Ad = 1200
:
150 + 60pi%2Ad = 1200
:
60pi%2Ad = 1200 - 150
:
60pi%2Ad = 1050
:
divide both sides by pi%2A60
d = 1050%2F%28pi%2A60%29
:
d = 5.57 inches is the diameter of the small wheel
then
8*5.57 = 44.56 inches is the diameter of the large wheel
:
:
See if this checks out, find no. of rotations of each wheel in 1200 inches
1200/(pi*5.57) = 68.58 times
1200/(pi*44.56) = 8.67 times
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rotates differs ~ 60 rotations