Question 1087754
Joe and Nancy decide to take a road trip. The first 120 miles of the drive is pretty​ easy, while the last 84 miles of the drive is filled with curves. They drove at an average of 9 miles per hour faster for the first 120 miles of the trip. The entire trip took 3 hours. How fast were Joe and Nancy driving for the first 120 miles of the​ trip?
<pre>Let speed during the 120-mile trip be S
Then speed during the 84-mile trip = S – 9
We then get the following TIME equation: {{{120/S + 84/(S - 9) = 3}}}
120(S – 9) + 84S = 3S(S – 9) -------- Multiplying by LCD, S(S – 9)
{{{120S - "1,080" + 84S = 3S^2 - 27S}}}
{{{3S^2 - 27S - 204S + "1,080" = 0}}}
{{{3S^2 - 231S + "1,080" = 0}}}
{{{3(S^2 - 77S + 360) = 3(0)}}}
{{{S^2 - 77S + 360 = 0}}}
(S - 72)(S - 5) = 0
S - 72 = 0               OR               S - 5 = 0
S, or {{{highlight_green(matrix(1,7, Speed, during, the, "120-mile", "trip:", 72, mph))}}}	         OR	      S = 5 (ignore)