Question 348728
Let {{{c}}} = circumference of the front wheel
Then {{{c + 3}}} = circumference of the rear wheel
When the front wheel travels {{{6000}}} ft, it makes
{{{6000/c}}} revolutions
The rear wheel makes {{{6000/c - 100}}} revolutions 
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{{{(6000/c - 100)*(c + 3) = 6000}}}
This says:
(revolutions of rear wheel)  x(circumference of rear wheel) = distance traveled
{{{6000 - 100c + 18000/c - 300 = 6000}}}
{{{6000c - 100c^2 + 18000 - 300c = 6000c}}}
{{{100c^2 + 300c - 18000 = 0}}}
{{{c^2 + 3c - 180 = 0}}}
Completing the square:
{{{c^2 + 3c + (3/2)^2 = 180 + (3/2)^2}}}
{{{c^2 + 3c + 9/4 = 720/4 + 9/4}}}
{{{(c + 3/2)^2 = 729/4}}}
{{{c + 3/2 = 27/2}}}
{{{c = 24/2}}}
{{{c = 12}}}
{{{c + 3 = 15}}}
The front wheel is 12 ft in circumference
The rear wheel is 15 ft in circumference
check:
{{{(6000/c - 100)*(c + 3) = 6000}}}
{{{(6000/12 - 100)*(12 + 3) = 6000}}} 
{{{(500 - 100)*15 = 6000}}}
{{{400*15 = 6000}}}
{{{6000 = 6000}}}