Rosa works due north of home. her husband juan 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 juan's distance from home. how far from home is juan?

This is a right triangle problem. c^2 = a^2 + b^2
Let b = 7 mi (Rosa's distance from home)
Let a = the east leg (Juan's distance from home
(a+1) = c (hypotenuse, distance between them)

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

FOIL (a+1)(a+1)
a^2 + 2a + 1 = a^2 + 49

Combine like terms
a^2 - a^2 + 2a = 49 - 1
2a = 48
a = 

a = 24 mi, Juan's distance from home

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