Question 887244
{{{d}}}= distance the carriage will have passed over when the front wheel has made 8 more revolutions than the rear wheel.
{{{d/2}}}= revolutions made by the front wheel.
{{{d/4}}}= revolutions made by the rear wheel.
The problem says that when the carriage passed over the distance {{{d}}} 
the front wheel will have made 8 ore revolutions than the rear wheel, so
{{{d/2=d/4+8}}}
Multiplying both sides of the equal sign times {{{4}}} gets rid of denominators, to get
{{{4*(d/2)=4(d/4+8)}}}--->{{{4*(d/2)=4(d/4)+4*8}}}--->{{{2d=d+32)}}}
Subtracting {{{d}}} from both sides of the equal sign gives us
{{{2d-d=d+32-d)}}}--->{{{highlight(d=32)}}}
The carriage will have passed over a distance of {{{highlight(32)}}} feet.
 
That would take {{{32/2=16}}} revolutions for the front wheel and {{{32/4=8}}} revolutions for the rear wheel.