To get from her home to a friend's house, Georgia must go past a school, then a post office:

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?

This item can be solved through ratio and proportion such that the ratio of the first trip (home to school to post office) and the time of travel should be equal to that of the second trip (post office to friend's house). This can be better expressed in the equation below,

(7/8 + 5/6) / 42 = x / 12

The value of x from the equation is 0.488 miles.

Given:

Georgia's home to school = 7/8 mile

School to post office = 5/6 mile

Whole trip takes 42 minutes.

Georgia's speed is 1 mile in 18 minutes.

Find the distance from the post office to her friend's house.

distance = speed x time; d = 1mile/18mins * 42 mins = 42mile/18 = 2.33 or 2 1/3 miles.

We can simplify 42/18 to 21/9 to 7/3

Let x be the distance from the post office to her friend's house.

7/8 + 5/6 + x = 7/3

x = 7/3 - 7/8 - 5/6

LCD = 24

x = [ (7/3) (8/8) ] - [ (7/8) (3/3) ] - [ (5/6) (4/4) ]

x = 56/24 - 21/24 - 20/24

x = (56-21-20) / 24

x = 11/24

The distance from the post office to her friend's house is 11/24 miles.