Question 1170197

a tour bus leaves sacramento every friday evening at 6:00 pm for a 270 mile trip to las vegas. due to mechanical problems the bus will be leaving at 6:30 pm today. to arrive in vegas at the same time, the driver must go 6 mph faster than usual. what is the buses normal speed ?
<pre>Let normal speed be S
Then faster speed is: S + 6
We then get the following TIME equation: {{{matrix(2,3, 270/(S + 6) + 30/60, "=", 270/S, 270/(S + 6) + 1/2, "=", 270/S)}}}
270S(2) + S(S + 6) = 270(2)(S + 6) ------- Multiplying by LCD, 2S(S + 6)
{{{matrix(3,3, 540S + S^2 + 6S, "=", 540S + "3,240", S^2 + 540S + 6S - 540S - "3,240", "=", 0, S^2 + 6S - "3,240", "=", 0)}}}
(S - 54)(S + 60) = 0
Normal speed, or {{{highlight_green(matrix(1,4, S, "=", 54, mph))}}}