Question 947776
______________________rate___________time______________distance
GO_____________________r_______________7_________________d
BACK__________________r+27_____________4_________________d


"average rate was 27 miles faster on the trip home,"
should be
"average rate was 27 miles-per-hour faster on the trip home,"



{{{system(r*7=d,(r+27)*4=d)}}}


{{{r=d/7}}}

Substitute into the BACK equation.
{{{(d/7+27)4=d}}}

{{{(d+27*7)*4=27d}}}

{{{4d+27*28=27d}}}

{{{27*28=23d}}}

{{{d=27*28/23}}}
{{{highlight(d=32&20/23)}}}-------YES!!!  THIS IS THE DISTANCE  BETWEEN HOME AND MOUNTAINS.