Question 1103345
The distance to the emporium is the same as from it to back home.




r, speed walking home
k=2, difference in speed to home versus to emporium
d=2
T=2&2/3, total time going plus returning
Question asks for r.

<pre>
             SPEED       TIME       DISTANCE

GOING          r+2      d/(r+2)       2

RETURNING       r       d/r           2

TOTAL                   {{{8/3}}}
</pre>

Solve for r:
{{{highlight_green(2/(r+2)+2/r=8/3)}}}

-

{{{1/(r+2)+1/r=4/3}}}

{{{3r+3r+6=4r^2+4r}}}

{{{4r^2-2r-6=0}}}

{{{highlight_green(2r^2-r-3=0)}}}

{{{(2r-3)(r+1)=0}}}

{{{2r-3=0}}}

{{{highlight(r=1&1/2)}}}