How far from home is Alan?

Question

Mary works due north of home. Her husband works due east. They leave for work at the same time. By the time Mary is 7 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 x be the distance of Alan from home.

Then the distance between Mary and Alan = x + 1

Using Pythagorean theorem, we get  7² + x² = (x + 1)²

Solving the equation we get x = 24 miles