[50 points (must answer in detail)] imogene's car traveled 660 mi averaging a certain speed. if the car had gone 6 mph faster, the trip would have taken 1 hour less. find the average speed.

55 mph

Step-by-step explanation:

Speed = Distance/Time so Time = Distance / Speed.

If the first speed is x mph, the first trip will take 660/x hours.

The second trip will take 660/(x+5) hours.

We want to find x such that (660/x) - 660/(x+5) = 1 (i.e. solving this equation for x).

Multiply both sides by x*(x+5):

660*(x+5) - 660x = x*(x+5)

660x + 3300 - 660x = x2 + 5x

x2 + 5x - 3300 = 0

(x - 55)*(x + 60) = 0

So either x = 55 or x = -60. Since x > 0, x = 55mph.

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