Question 1029727

Chris went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he would have arrived 9 hours sooner. How fast did he actually ride?
<pre>Let his actual speed be S
Actual time taken: {{{24/S}}}
If he'd traveled 6 mph faster, his speed would've been: S + 6
Time that he would’ve taken, travelling at the faster speed: {{{24/(S + 6)}}}
We then get the following TIME equation: {{{24/S = 24/(S + 6) + 9}}}
24(S + 6) = 24S + 9S(S + 6) ------- Multiplying by LCD, S(S + 6)
{{{24S + 144 = 24S + 9S^2 + 54S}}}
{{{24S + 9S^2 + 54S - 24S - 144 = 0}}}
{{{9S^2 + 54S - 144 = 0}}}
{{{9(S^2 + 6S - 16) = 9(0)}}} ----- Factoring out GCF, 9
{{{S^2 + 6S - 16 = 0}}}
(S - 2)(S + 8) = 0
S, or actual speed = {{{highlight_green(2)}}} mph