SOLUTION: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
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Question 149544: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!
200 miles
x speed
y time
200/x=y
200/(x+10)=y-1
Plug in y in the second equation
200/(x+10)=200/x-1
Common denominator on the right side x
200/(x+10)=200/x-x/x
Subtract the numerators
200/(x+10)=(200-x)/x
Cross multiply
200x=-x^2+190x+2000
Subtract 200x from both sides
0=-x^2-10x+2000
Take out negative one
0=-1(x^2+10x-2000)
Factor
0=-1(x+50)(x-40)
Set each equal to zero and solve
(x+50)=0
x=-50
(x-40)=0
x=40
Speed can't be negative, so x=40.
Original speed: 40 mph
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