Question 965068
Greg drove at a constant speed in a rainstorm for 294 miles. He took a break, and the rain stopped. He then drove 156 miles at a speed that was 3 mph faster than his pervious speed. If he drove for 9 hours, find the cars speed for each part of the trip.
<pre>Let speed during 1st leg of trip, be S
Then speed during 2nd leg = S + 3
Time taken to complete 1st leg: {{{294/S}}}
Time taken to complete 2nd leg: {{{156/(S + 3)}}}
We then get: {{{294/S + 156/(S + 3) = 9}}}
294(S + 3) + 156S = 9(S)(S + 3) ------- Multiplying by LCD, S(S + 3)
{{{294S + 882 + 156S = 9S^2 + 27S}}}
{{{450S + 882 = 9S^2 + 27S}}}
{{{9S^2 + 27S - 450S - 882 = 0}}}
{{{9S^2 - 423S - 882 = 0}}}
{{{9(S^2 - 47S - 98) = 9(0)}}}
{{{S^2 - 47S - 98 = 0}}}
(S - 49)(S + 2) = 0  
S, or speed on 1st leg = {{{highlight_green(49)}}} mph            OR           S = - 2 (ignore)
Speed on 2nd leg: 49 + 3, or {{{highlight_green(52)}}} mph