SOLUTION: 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 m

Algebra ->  Functions -> SOLUTION: 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 m      Log On


   

Question 570532: 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?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can form a right triangle of this situation with Rosa's distance from home (5 miles) as the height and Ray's distance from home as the base (call it x miles). The distance between them is represented by the hypotenuse of the right triangle (call this x+1 miles).
Invoking the Pythagorean theorem (c%5E2+=+a%5E2%2Bb%5E2) where: c+=+x%2B1, a+=+5, and b+=+x we'll solve for x:
%28x%2B1%29%5E2+=+5%5E2%2Bx%5E2
x%5E2%2B2x%2B1+=+25%2Bx%5E2 Subtract x%5E2 from both sides.
2x%2B1+=+25 Subtract 1 from both sides.
2x+=+24 Divide by 2.
x+=+12
Ray is 12 miles fom home.