SOLUTION: How do I solve for x in this word problem? Jim made a 450 mile trip in his car at a certain speed. If he had gone 10 mph faster, he could have made the trip in one hour less ti

Question 311612: How do I solve for x in this word problem?
Jim made a 450 mile trip in his car at a certain speed. If he had gone 10 mph faster, he could have made the trip in one hour less time. Find his speed.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Jim made a 450 mile trip in his car at a certain speed. If he had gone 10 mph faster, he could have made the trip in one hour less time. Find his speed.
.
let the initial speed be x
the time he took was 450/x
.
if speed increases by 10 mph
his speed will be x+10.
time he will take = 450/x+10
.
450/x -1 = 450 / x+10
450/x -450/ x+10= 1
LCM = x(x+10)
450(x+10)-450x=x(x+10)
450x+4500-450=x^2+10x
x^2+10x-4500=0
find x1 x2
x1= -10+sqrt(100+18000) /2
=62.2 mph
x2 = -10-sqrt(100+18000) /2
x2=-72.2
.
So his speed was 62.2 mph.
After increase his speed would have been 72.2.
CHECK
.
(450/62.2)-(450/72.2)=1

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