SOLUTION: two runners start at a certain point simultaneously, going the the same directions, the speed fo one runner is two thirds of the speed of the other runner. if at the end of 3 hour

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Question 429498: two runners start at a certain point simultaneously, going the the same directions, the speed fo one runner is two thirds of the speed of the other runner. if at the end of 3 hours they are 6 miles apart, what is the speed of each runner?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
one runner speed = x mph
otehr runner speed = 2x/3
..
difference in speeds = x-2x/3
=x/3

distance = 6 miles
time = 3 hours
6/x= 3
x=2 mph
2x/3 = 4 /3 mph


Answer by ikleyn(53427) About Me  (Show Source):
You can put this solution on YOUR website!
.
Two runners start at a certain point simultaneously, going the same directions, the speed for one runner is two thirds
of the speed of the other runner. If at the end of 3 hours they are 6 miles apart, what is the speed of each runner?
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        The solution of the other tutor is incorrect.
        I came to bring a correct solution. 


Let x be "One" runner speed, in mph.

Then the "other" runner speed is  %283%2F2%29x mph  <<<---===  it is the true meaning of the problem's condition.


The "distance " equation is

    3%2A%28%283%2F2%29x%29 - 3x = 6  miles  (the difference of the ran distances in 3 hours)


Simplify and find x

    %289%2F2%29x - 3x = 6,

    9x - 6x = 12,

       3x   = 12,

        x   = 12/3 = 4.


Answer.  The slower runner' speed is 4 mph.  The faster runner' speed is  %283%2F2%29%2A4 = 3*2 = 6 mph.

Solved correctly.