Runner A Is Initially 6.0 Km

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 initially 5 km east of the flagpole and is running west at a constant velocity of 8 km/h. What will be the position of the 2 runners from the flagpole when their paths cross.

Please use GUESS method and explain.

Expert Answers
ndnordic eNotes educator| Certified Educator

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.