Question 1205894
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A and B are running a race. A has an 84 feet head start when they begin running. 
B runs 12 feet while A covers 8 feet. Determine distance A runs before B overtakes A.
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<pre>
Let d be the distance A runs before B overtakes A.

Then the distance that B will cover at that time moment is (d+84) feet.


Their speeds are in the ratio {{{speed_A/speed_B}}} = {{{8/12}}} = {{{2/3}}}.

They spend the same time - THEREFORE, the ratio of distances is the same 
as the ratio of their speeds.


So, we write this proportion

    {{{d/(d+84)}}} = {{{2/3}}}.


Cross-multiply

    3d = 2*(d+84).


Simplify and find d

    3d = 2d + 2*84

    3d - 2d = 2*84

       d    = 168.


<U>ANSWER</U>.  The distance A runs before B overtakes A is 168 feet.
</pre>

Solved.


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Just fixed my error.

Thanks to @greenestamps !