Rosa works due north of home. Her husband Ray works due east. They leave for work at the same time. By the time Rosa is 5 miles from home, the distance between them is one mile more than Ray 's distance from home. How far from home is Ray Ray ?

Ray is 12 miles from home.

Let x be Ray's distance from home. His distance is one leg of a right triangle; 5, Rosa's distance from home, is the other. The hypotenuse, the distance between them, is 1 more than Ray's distance from home, or x+1. Using the Pythagorean theorem,

5²+x² = (x+1) ²

25+x² = (x+1) (x+1)

Multiplying the binomials, we have

25+x²=x*x+1*x+1*x+1*1

25+x²=x²+1x+1x+1

25+x²=x²+2x+1

Subtracting x² from both sides,

25 = 2x+1

Subtracting 1 from both sides,

24 = 2x

Divide both sides by 2, and we have

12 = x

Ray is 12 miles from home.