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 149897This question is from textbook
: 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. This question is from textbook

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
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=x%5E2%2B10x


Subtract on the right
%28200x%2F%28x%5E2%2B10x%29%29=%28%28200x-2000-x%5E2-10%29%2F%28x%5E2%2B10x%29%29

Eliminate the denominator.
Subtract 200x from both sides

0=2000-x%5E2-10x
Reorder the right side
0=-x%5E2-10x%2B2000

Take out a ngeative one
0=-1%28x%5E2%2B10x-2000%29

Factor
0=-1%28x%2B50%29%28x-40%29

Solve
x=-50
x=40

since speed can't be negative, x=40, so

40 mph