To get from her home to a friend's house, Georgia must go past a school, then a post office: [asy]
size(9cm);
dot((0,0)); dot((7/8,0)); dot((41/24)); dot((7/3,0)); draw((0,0)--(7/3,0));
label(rotate(45)*"Home~",(0,0),SW);
label(rotate(45)*"School~",(7/8,0), SW);
label(rotate(45)*"Post office~",(41/24,0),SW);
label(rotate(45)*"Friend's house~",(7/3,0),SW);
[/asy]

Signs tell Georgia that the distance she walks from home to the school is $7/8$ mile, and the distance from the school to the post office is $5/6$ mile.

The whole trip takes Georgia $42$ minutes. If Georgia can walk a mile in $18$ minutes, then how many miles is the distance from the post office to her friend's house?