SOLUTION: a tour bus leaves sacremento every friday evening at 5:00 pm for a 270 mile trip to las vegas. this week, however, the bus leaves at 5:30 pm. to arrive in las vegas on time, the dr

Let x be that unknown regular speed under the question.


Then you have this "time" equation

     -  = 0.5  of an hour  (or 30 minutes).     (1)



You may multiply both sides by x*(x+6); reduce to the standard form quadratic equation and then solve it to find x.



I will solve this equation MENTALLY.

For it, I will multiply both sides by 2. I will get then

     -  = 1,


and then the solution  x= 54 becomes OBVIOUS.



ANSWER.  The regular speed is 54 miles per hour.


CHECK.  Then equation (1)  takes the form   -  =  5 - 4.5 = 0.5  hour, confirming the answer.