Runner A is initially 10.0 mi west of aflagpole and is running with a constant v

Question

Runner A is initially 10.0 mi west of aflagpole and is running with a constant velocity of 2.0 mi/h due east. Runner B is initially 1.0 mi east of the flagpole and is running with aconstant velocity of 8.0 mi/h due west.How far are the runners from the flagpole when they meet?

I have been trying to set location of A and B equal at a certaintime, but having some difficulty working it out.

Explanation / Answer

Hi,     Let the two runners at a distance of x from theflag pole when they meet.     Then the runner A has traveled a distance of10mi - x     Runner B traveled a distance of 1mi + x     but distance traveled = velocity *time.     therefore 10mi - x = (2mi/h)t-------------(1)        and 1mi + x =(8mi/h)t       -------------(2) Multiplying (1) with 4 we get        40mi - 4x = (8mi/h)t-------------------(3) (2)=>1mi + x = (8mi/h)t ------------------------- sub:   41mi -5x = 0 Then x = 41mi/5            =8.2mi. therefore when they meet each other they are at distance of 8.2mifrom the flagpole. Hope this helps you.

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