SOLUTION: Two wheels have diameters of 12 inches and 18 inchesrespectively.Both wheels roll along parallel straight lines at the same linera speed until the large wheel has revolved 72 times

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Question 867940: Two wheels have diameters of 12 inches and 18 inchesrespectively.Both wheels roll along parallel straight lines at the same linera speed until the large wheel has revolved 72 times.At this point,how many times has the small wheel revolved?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the circumference of the small wheel =
+C%5B1%5D+=+pi%2Ad%5B1%5D+
Let the circumference of the large wheel =
+C%5B2%5D+=+pi%2Ad%5B2%5D+
You are given that:
+d%5B1%5D+=+12+ in
+d%5B2%5D+=+18+ in
------------------------
With each revolution, a wheel traces it's
circumference onto the flat ground
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With +72+ revolutions, the large wheel
traces +72%2AC%5B2%5D+=++72%2Api%2A18+
---------------------------------------
The small wheel, since it's rolling with the
large wheel has to trace out the same
linear distance. It must also make more
revolutions ( turning faster ).
I'll say it makes +n+ revolutions
+72%2Api%2A18+=+n%2Api%2A12+
+1296+=+12n+
+n+=+108+
The small wheel has revolved 108 times