Question 58873
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. 
:
you have the right idea:
Original time - 1 hr = time going faster
The equation as you stated it:
{{{600/x - 1}}} = {{{600/(x+20)}}}
:
To solve for x you must get rid of those denominators, you do this by mult the
equation by x(x+20), a common denominator, you then have:
:
600(x+20) - 1(x(x+20) = 600x
:
600x + 12000 - x^2 - 20x = 600x
:
-x^2 + 600x - 600x - 20x + 12000 = 0
:
-x^2 - 20x + 12000 = 0
:
x^2 + 20x - 12000 = 0; Mult eq by -1, easier to factor when x^2 is positive
:
Factors to:
(x + 120)(x - 100) = 0
:
x = +100, the positive solution is what we want here:
:
:
We can check that using time:
(600/100) - 1 = (600/120)
6 - 1 = 5