Question 1004816
<pre>
4.5:1 = 64:x

{{{4.5/1}}}{{{""=""}}}{{{64/x}}}

{{{expr(2/2)}}}{{{""*""}}}{{{4.5/1}}}{{{""=""}}}{{{64/x}}}

{{{9/2}}}{{{""=""}}}{{{64/x}}}

{{{9x}}}{{{""=""}}}{{{128}}}

{{{x}}}{{{""=""}}}{{{128/9}}}

{{{x}}}{{{""=""}}}{{{14&2/9}}}

But no gear can have a fraction for its 
number of teeth.  So the problem is
botched or it wasn't copied correctly.

If it were the smaller gear that has
64 teeth, then the problem would have
a solution:

4.5:1 = 64:x

{{{4.5/1}}}{{{""=""}}}{{{x/64}}}

{{{expr(2/2)*expr(4.5/1)}}}{{{""=""}}}{{{x/64}}}

{{{9/2}}}{{{""=""}}}{{{x/64}}}

{{{2x}}}{{{""=""}}}{{{576}}}

{{{x}}}{{{""=""}}}{{{576/2}}}

{{{x}}}{{{""=""}}}{{{288}}}

The larger (not "longer") gear would have 288 teeth.

Edwin</pre>