Question 80653
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.
y=time
xy=600
(x+20)(y-1)=600
Now what do I do?
:
I would do it this way:
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Let x = original speed
Then (x+20) = faster speed (as you had)
: 
Write a time equation: Time = dist/speed
:
Original time - 1 = Faster time
{{{(600/x)}}} - 1 = {{{600/(x+20)}}}
:
Multiply equation by x(x+20) and you have:
600(x+20) - x(x+20) = 600x
:
600x + 12000 - x^2 - 20x = 600x
:
-x^2 - 20x + 600x - 600x + 12000 = 0
:
-x^2 - 20x + 12000 = 0
:
x^2 + 20x - 120000 = 0: multiplied equation by 0 (easier to factor)
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Factors to:
(x+120)(x-100) = 0
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x = +100, the positive solution is what we want here
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Check:
600/100 - 1 = 600/120; proves our solution