Question 942720

Maureen can run at a rate that is 2 miles per hour faster than her friend Hector's rate. While training for a mini marathon, Maureen gives Hector a half-hour head start and then begins chasing Hector on the same route. If Maureen passes Hector 12 miles from the starting point, how fast is each running?
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Let Maureen’s speed be S
Then Hector’s is: S - 2
Since she passed Hector 12 miles from the starting point and with Hector getting a ˝ hr head start,
we get: {{{12/S - 1/2 = 12/(S - 2)}}}
12(2)(S – 2) – S(S – 2) = 12(2S) ---- Multiplying by LCD, 2S(S – 2)
{{{24S - 48 - S^2 + 2S = 24S}}}
{{{26S - 48 - S^2 = 24S}}}
{{{S^2 + 24S - 26S + 48 = 0}}}
{{{S^2 - 2S + 48 = 0}}}
(S - 8)(S + 6) = 0
S, or Maureen’s speed = {{{highlight_green(8)}}} mph                OR                S = - 6 (ignore)
Hector’s speed: 8 – 2, or {{{highlight_green(6)}}} mph