SOLUTION: Imogene's car traveled 770 mi averaging a certain speed. If the car has gone 7 mph faster, the trip would have taken 1 hour less. Find the average speed.

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Question 969347: Imogene's car traveled 770 mi averaging a certain speed. If the car has gone 7 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+ = her normal speed in mi/hr
+s+%2B+7+ = her faster speed in mi/hr
Let +t+ = her time in hours
when traveling at +s+ mi/hr
+t+-+1+ = her time in hours when
traveling at +s+%2B+7+ mi/hr
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Equation for traveling at normal speed
(1) +770+=+s%2At+
Equation for traveling at faster speed
(2) +770+=+%28+s%2B7+%29%2A%28+t+-+1+%29+
--------------------------
(2) +770+=+s%2At+%2B+7t+-+s+-+7+
and
(1) +s+=+770%2Ft+
(2) +770+=+%28+770%2Ft+%29%2At+%2B+7t+-+770%2Ft+-+7+
(2) +770+=+770+%2B+7t+-+770%2Ft+-+7+
(2) +0+=+7t+-+770%2Ft+-+7+
(2) +770%2Ft++=+7t+-+7+
Multiply both sides by +t+
(2) +770+=+7t%5E2+-+7t+
(2) +7t%5E2+-+7t+-+770+=+0+
(2) +t%5E2+-+t+-+110+=+0+
(2) +%28+t+-+11+%29%2A%28+t+%2B+10+%29+ ( by looking at it )
+t+=+11+ ( time must be positive )
and
(1) +s+=+770%2Ft+
(1) +s+=+770%2F11+
(1) +s+=+70+
the average speed is 70 mi/hr
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check:
(2) +770+=+%28+s%2B7+%29%2A%28+t+-+1+%29+
(2) +770+=+%28+70%2B7+%29%2A%28+11+-+1+%29+
(2) +770+=+77%2A10+
(2) +770+=+770+
OK