Runner A is initially 6 km west of a flagpole and is running with a constant velocity of 9 km/hr due east.?

Question

runner b is initially 5 km east of the flagpole and is running with a velocity of 8 km/hr due west. What will be the distance of the two runners from the flagpole when their paths cross?

Please answer in kilometers:)

Answer 1

Their total separation is 11 km and their net speed of approach is 17 km/hr hence they meet in 11/17 hr.  At that time, runner A has traveled 9 km/hr * 11/17 hr = 5.824 km.  That means he is 6 - 5.824 = 0.176 km from the pole.  You can check for B and find that he is also the same distance away.

Answer 2

I drew a diagram ... it made this problem much easier to visualize. Runner A starts out 6 km west of the flagpole and Runner B starts out 5km east of the flagpole; they are 11km apart at t=0. Because Runner A is running at 9 km/hr, I divided his distance into thirds ... in 20 min he is at 3km (still 3 km away), in 40 min he is at 6km (he is at the flagpole), and in 60 min he is 3km east of the flagpole. I divided Runner B's travel into fourths because he is running at 8km/hr. As a result, runner B is 2km from his start in 15 min, 4km from his start (1km east of flagpole) in 30 min, 6 km from start (1 km west of flagpole) in 45 minutes, and 8km from his start (3km west of the flagpole) in 60 min. According to this timeline, Runner A is at the flagpole in 40 minutes. Where is Runner B in 40 minutes? Multiply 8km/60min  x  40 min = 5.33 km (which is .33km west of the flagpole). The runners have passed each other at the 40min mark and are .33km apart at this time.