Answer:
To the nearest mile, Tony and Jim are 9 miles apart.
To visualize this, imagine a right triangle where Jim's starting point is at the right angle. Tony travels 5 miles due south, which is the adjacent side of the triangle. Jim travels 6 miles north east, which is the hypotenuse of the triangle. The opposite side of the triangle is the distance between Tony and Jim.
Using the Pythagorean theorem, we can find the length of the opposite side:
opposite side = sqrt(hypotenuse^2 - adjacent side^2)
opposite side = sqrt(6^2 - 5^2)
opposite side = sqrt(11)
To the nearest mile, the distance between Tony and Jim is 9 miles.