Question 537930
Use the distance formula:
{{{d = r*t}}} where: d = distance, r = rate(speed), and t = time of travel.
Going to the store:
{{{d[1] = r[1]*t[1]}}} Substitute: {{{r[1] = 6}}}
{{{d[1] = 6*t[1]}}}
Returning returning from the store:
{{{d[2] = r[2]*t[2]}}} Substitute {{{r = 4}}}
{{{d[2] = 4*t[2]}}} 
Now the total time is {{{t[1]+t[2] = 10}}} so {{{t[2] = 10-t[1]}}} and the distance to the store is the same as the distance back, so {{{d[1] = d[2]}}}
So now we can write:
{{{6*t[1] = 4*t[2]}}} Substitute {{{t[2] = 10-t[1]}}}
{{{6*t[1] = 4(10-t[1])}}} Simplify and solve for {{{t[1]}}}
{{{6*t[1] = 40-4*t[1]}}} Add {{{4*t[1]}}} to both sides.
{{{10*t[1] = 40}}} Divide both sides by 10.
{{{t[1] = 4}}} Now substitute this into the first equation and solve for {{{d[1]}}}
{{{d[1] = 6*t[1]}}} Substitute {{{t[1] = 4}}}
{{{d[1] = 6*4}}}
{{{d[1] = 24}}}
The store is 24 miles away.