SOLUTION: Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 16 feet larger than that of smaller circle and the ratio of the circumferences is 15:1,

Let R be the radius of the larger circle, in feet;
then the radius of the smaller circle is (R-16) feet. 


The ratio of the circumferences is the same as the ratio of radii; 
so we can write a proportion

     = .


To find R, cross-multiply

    R = 15*(R-16),


then simplify

    R = 15R - 240

    240 = 15R - R

    240 = 14R,

     R  =   =  = 17 ft (rounded).


ANSWER.  Greater radius is  17 ft.

         Smaller radius is  1 ft.


CHECK.  17 : 1 =  = 15.  ! correct !