From their office, Cathy drives due west while John drives south. When John is 7 mi from the office, the distance between them is 1 mi more than Cathy’s distance from the office. Find the distance between Cathy and John.
Let x represent the distance between Cathy and John. The geometry of the problem makes that distance be the hypotenuse of a right triangle with legs 7 and (x -1). Then x is the solution to .. x^2 = (x -1)^2 +7^2 . . . . Pythagorean theorem .. 0 = -2x +1 +49 . . . . . . . eliminate parentheses and subtract x^2 .. 2x = 50 . . . . . . . . . . . . . simplify and add 2x .. x = 25 . . . . . . . . . . . . . . divide by 2
