Problema Solution
Mary works due north of home. Her husband Alan works due east. They leave for work at the same time. By the time Mary is 3 miles from home, the distance between them is one mile more than Alan's distance from home. How far from home is Alan?
Answer provided by our tutors
Let "x" be Alan's distance from home.
Draw the "north" and "east" arrows, and a slanty line showing the distance between them. This should form a right triangle.
Label Fran's side as "3", Alan's side as "x", and the hypotenuse as "x + 1".
Then the Pythagorean Theorem gives us:
3^2 + x^2 = (x + 1)^2
9 + x^2 = x^2 + 2x + 1
9 = 2x + 1
8 = 2x
4 = x
Then Alan is four miles from home.