SOLUTION: Imogene's car traveled 576 mi averaging a certain speed. If the car had gone 8 mph faster the trip would have taken 1 hour less. Find the average speed.

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Question 316082: Imogene's car traveled 576 mi averaging a certain speed. If the car had gone 8 mph faster the trip would have taken 1 hour less. Find the average speed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The average speed is (total distance)/(total time)
Let s = her average speed speed
Let t = the time for the trip
given:
576+=+s%2At
576+=+%28s+%2B+8%29%2A%28t+-+1%29
576+=+s%2At+%2B+8t+-+s+-+8
By substitution:
576+=+576+%2B+8t+-+s+-+8
0+=+8t+-+s+-+8
s+=+8t+-+8
Substituting again:
576+=+8%2A%28t+-+1%29%2At
72+=+%28t+-+1%29%2At
t%5E2+-+t+-+72+=+0
Using quadratic formula:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-72%29+%29%29%2F%282%2A1%29+
t+=+%28+1+%2B-+sqrt%28+1+%2B+288+%29%29+%2F+2+
t+=+%281+%2B+17%29%2F2 (ignore the negative root)
t+=+9
And, since
576+=+s%2At
576+=+9s
s+=+64
Her average speed for the trip is 64 mi/hr