math word problem

Question

Rosa works due north of home. Her husband Alan
works due east. They leave for work at the same time. By the time
Rosa is 7 miles from? home, the distance between them is one mile more than
Alan's distance from home. How far from home is Alan

 

Answer 1

H is where home is

R is where Rosa is

A is where Alan is

the three form a right triangle

let n=distance Alan is from home

n+1 is the distance between Rosa and Alan (the hypotenuse)

7 is the distance Rosa is from home

use the Pythagorean Theorem

(n+1)^2=7^2+n^2

n^2+2n+1=49+n^2

subtract n^2 from both sides

2n+1=49

2n=48

n=24

Alan is 24 miles from home