SOLUTION: Imogene's car traveled 624 miles averaging a Certain speed. If the car had gone 4 mph faster the trip would have taken 1 hour less. Find the average speed. 

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Question 563293: Imogene's car traveled 624 miles averaging a
Certain speed. If the car had gone 4 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!
Let +s+ = speed of the car
Let +t+ = time for trip
given:
(1) +624+=+s%2At+
(2) +624+=+%28+s+%2B+4+%29%2A%28+t+-+1+%29+
-----------------------
(2) +624+=+s%2At+%2B+4t+-+s+-+4+
and
(1) +t+=+624%2Fs+
Substitute this into (2)
(2) +624+=+s%2A%28+624%2Fs+%29+%2B+4%2A%28+624%2Fs+%29+-+s+-+4+
(2) +624+=+624+%2B+2496%2Fs+-+s+-+4+
(2) +2496%2Fs+=+s+%2B+4+
(2) +2496+=+s%5E2+%2B+4s+
(2) +s%5E2+%2B+4s+-+2496+=+0+
Use quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+4+
+c+=+-2496+
+s+=+%28-4+%2B-+sqrt%28+4%5E2+-+4%2A1%2A%28-2496%29+%29%29+%2F+%282%2A1%29+
+s+=+%28-4+%2B-+sqrt%28+16+%2B+9984+%29%29+%2F+2+
+s+=+%28-4+%2B-+sqrt%28+10000+%29%29+%2F+2+
+s+=+%28-4+%2B+100%29+%2F+2+
+s+=+96%2F2+
+s+=+48+ ( I can ignore the (-) square root )
Her average speed is 48 mi/hr
check answer:
(1) +624+=+s%2At+
(1) +624+=+48t+
(1) +t+=+13+
and
(2) +624+=+%28+48+%2B+4+%29%2A%28+13+-+1+%29+
(2) +624+=+52%2A12+
(2) +624+=+624+
OK