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Runner A is initially 3 mi west of a flagpole and is running with a constant velocity of 6.4 mi/h due east. Runner B is initially 2.4 mi east of the flagpole and is running with a constant velocity of 6.7 mi/h due west. How far are the runners from the flagpole when their paths cross? Anwser in units of mi.
 
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HallsofIvy

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This should be relatively easy since everything- the runners, the flagpole, and their paths are all on a straight line. No vectors or trigonometry needed!

First, how far apart are the two runners when they start?
The problem tells you that one is 3 mi west and the other 2.4 miles east of the flag pole: draw a picture.

You also know how fast the two runners are running toward each other
Since they are running directly towards each other, their combined speed is 6.4+ 6.7= 13.1 mph. You know the distance between them and you know the speed with which they are "closing". How long do they run until they meet? In other words, what is t when when 13.1 t is equal to the original distance between them.

Since you are asked for the position when they meet, you will know have to find how far either one is from the flagpole at that time.
Since A starts 3 mi from the flagpole and runs at 6.4 mph, his distance from the flagpole at time t is 3- 6.4 t. (What does it mean if putting in the t you got above makes this negative?)
 

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