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.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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.      Log On


   

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) About Me  (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