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.

Not sure how to solve.

Let distance A travels before being overtaken by B, be D
Since A is already 84 feet ahead of B, then distance B travels to overtake A = "D + 84" feet
Since B's speed is 12 feet, per time period, B's time to get to "catch-up" point = {{{(D + 84)/12}}}
Also, since A's speed is 8 feet, per time period, A's time to get to "catch-up" point = {{{D/8}}}
Because the time they take to get to the catch-up point is the same, we get: {{{matrix(1,3, (D + 84)/12, "=", D/8)}}}
                                            2(D + 84) = 3D ----- Multiplying by LCD, 24
                                           2D + 2(84) = 3D
                                                2(84) = 3D - 2D
Distance A travels before being overtaken by B, or {{{highlight_green(matrix(1,5, D, "=", 2(84), "=", highlight(matrix(1,2, 168, feet))))}}}</pre>