Fran works due north of home. Her husband Juan works due east. By the time Fran is 5 miles from home the distance between them is one mile more than Juan's distance from home. How far from home is Juan?

If I understood the question correctly, let's set the coordinates (5,5) from the origin (the home). To find the longer side of the triangle, (the distance between the husband and wife), we use A squared * B squared = C squared. 25*25=625, the square root of 625 is 25. So the distance between the husband and wife would be 25 miles. Therefore, one mile less than their distance would be 24 miles. To answer your question, Juan is 24 miles from home.