Question 867940
Let the circumference of the small wheel =
{{{ C[1] = pi*d[1] }}}
Let the circumference of the large wheel =
{{{ C[2] = pi*d[2] }}}
You are given that:
{{{ d[1] = 12 }}} in
{{{ d[2] = 18 }}} in
------------------------
With each revolution, a wheel traces it's
circumference onto the flat ground
---------------------------------------
With {{{ 72 }}} revolutions, the large wheel
traces {{{ 72*C[2] =  72*pi*18 }}}
---------------------------------------
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*pi*18 = n*pi*12 }}}
{{{ 1296 = 12n }}}
{{{ n = 108 }}}
The small wheel has revolved 108 times