This is a physics question.Runner A is initially 6 km west of a flagpole and running at a constant velocity of 9.0 km/h due east. Runner B is...

The GUESS method stands for givens, unknowns, equation,
substitution, and solution.

In your
problem:

G - givens are:  initial position of each runner
in relation to a reference point (flag pole) - for A this is 6 km and for B this is 5
km  (this means they are 11 km apart); and the velocity of each runner.  V(A) = 9 km/hr 
and V(B) = 8 km/hr.

U - unknown is where, in relation to
the flagpole, will the two runner meet.

"E - equation.  let
X = distance that runner A has gone when they meet. then 11-X = distance runner B has
gone.  Using the formula time = distance/velocity;  for runner A time = X/V(A) and for
runner B time = (11-X)/V(B).  Since times are equal for the two runners, the final
equation is:

X/V(A) =
(11-X)/V(B)

S -
substitution

X/9 km/hr = (11 - X)/8
km/hr

S -  Solve.

X = 5.82
km

This means that runner A has moved 5.82 km east from his
starting point of 6 km.  6 - 5.82 means he is 0.18 km west of the
flagpole.

For runner B he has moved 11-5.82 km west from
his starting point.  11-5.82 = 5.18 km west. Since he started 5 km east, he is now 0.18
km west of the flagpole also.