SOLUTION: Amy travels 450 miles at a certain speed. If the car had gone 15mph faster, the trip would have taken one hour less. Find Amy's speed. A. 78 mph B. 75 mph C. 68 mph D. 72 mph

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Question 22908: Amy travels 450 miles at a certain speed. If the car had gone 15mph faster, the trip would have taken one hour less. Find Amy's speed.
A. 78 mph
B. 75 mph
C. 68 mph
D. 72 mph
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
LET AMY'S SPEED BE X MPH….TIME TO TRAVEL 450 MILES=450/X HRS.
IF CAR GOES 15 MPH FASTER SPEED = X+15…..TIME TO TRAVEL=450/(X+15)
THIS TIME IS 1 HOUR LESS.SO…450/X-450/(X+15)=1…MULTIPLYING BY LCM X(X+15)
450{X+15-X)=X(X+15)=450*15=6750=X^2+15X
X^2+15X-6750=0=X^2+90X-75X-6750=X(X+90)-75(X+90)=(X-75)(X+90).HENCE X=75….B IS THE ANSWER.