SOLUTION: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle

Question 114060: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle,
:
Let x = his actual speed
Then
(x+20) = the faster speed, that would have reduced the time by 1 hr
:
Write a time equation:
Time =
:
Actual time = faster time + 1 hr
= + 1
:
Multiply equation by x(x+20) to get rid of the denominators:
x(x+20)* = x(x+20)* + x(x+20)(1)
:
Cancel out the denominators and you have;
600(x+20) = 600x + x(x+20)
:
600x + 12000 = 600x + x^2 + 20x
:
Arrange as a quadratic equation on the right
0 = x^2 + 20x + 600x - 600x - 12000
:
x^2 + 20x - 12000 = 0
:
Factors to:
(x+120)(x-100) = 0
Positive solution:
x = 100 mph actual speed
:
:
Check by finding the times of the two speeds
600/100 = 6 hr
600/120 = 5 hrs
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