Question 1045132
{{{n}}}= number of turns for the rear wheel
Since the front wheel rotated 10 times more than the rear wheel,
{{{n+10}}}= number of turns for the front wheel.
Since the circumference of the rear wheel, in meters, is {{{6}}} ,
each turn of the rear wheel makes the vehicle advance {{{6}}} meters.
So, {{{6n}}}= distance traveled by the vehicle, in meters.
Similarly, each turn of the from wheel corresponds to {{{4}}} meters of distance traveled.
So, we can also say that
{{{4(n+10)}}}= distance traveled by the vehicle, in meters.
Because we are talking about the same distance
{{{6n=4(n+10)}}} .
We just havwe to solve that equation to find {{{n}}} ,
and then we can calculate {{{6n}}}= distance traveled by the vehicle, in meters.
To verify that we solved teh problem correctly, we can also calculate
{{{4(n+10)}}}= distance traveled by the vehicle, in meters,
and it should be the same distance.


{{{6n=4(n+10)}}}
{{{6n=4n+40)}}}
{{{6n-4n=40)}}}
{{{2n=40)}}}
{{{n=40/2}}}
{{{n=20}}}
So, the rear wheel turned {{{20}}} times,
and the distance traveled by the vehicle, in meters, is
{{{6*20=highlight(120)}}} .


Verification:
If the rear wheel turned {{{20}}} times,
the front wheel must have turned {{{20+10=30}}} times.
with each turn of the front wheel corresponding to the vehicle advancing {{{4}}} meters,
{{{30}}} turns of the front wheel correspond to a distance traveled by the vehicle, in meters, of
{{{4*30=120}}} .