Question

Fran

Fran works due north of home. Her husband
Alan
Alan works due east. They leave for work at the same time. By the time

Fran is

5 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

Let a represent Alan's distance from home at the time of interest. By the Pythagorean theorem,
.. (a +1)^2 = a^2 +5^2
.. a^2 +2a +1 = a^2 +25
.. 2a = 24
.. a = 12

Alan is 12 miles from home.