Steve traveled 200 miles at a certain speed Had he gone 10mp

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.

Solution

Steve DATA:
distance=200 miles ; rate= x mph ; time = d/r=200/x hrs
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New Steve DATA:
distane = 200 miles ; rate = x+10 mph ; time=d/r = 200/(x+10)
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EQuATIOn:
old time = new time + 1 hr.
200/x = 200/(x+10) + 1
200(x+10) = 200x +x(x+10)
200x+2000=200x+x^2+20x
x^2+20x-2000=0
x=[-20+sqrt(400-4*-2000)]/2
x=71.65/2
x=35.83 mph (old speed)
x+10; 45.83 mph (new speed)