Question 149799: I NEED HELP I AM REALLY STUMPED ON THIS SOLUTION!!
Steve traveled 200 miles at a certain speed. Had he gone 10 mph faster, the trip would have taken one hour less. Find the speed of his vehicle.
I am having a tough time. Thank you in advance to anyone who can help me.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Let x = speed of vehicle
.
Time to travel 200 miles is
200/x
.
Time to travel 200 miles, if he went 10 mph faster:
200/(x+10)
.
From:"Had he gone 10 mph faster, the trip would have taken one hour less." we get:
200/x - 1 = 200/(x+10)
multiplying both sides by (x+10):
(x+10)(200/x - 1) = 200
multiplying both sides by x:
(x+10)(200 - x) = 200x
200x + 2000 -x^2 - 10x = 200x
2000 -x^2 - 10x = 0
x^2 + 10x - 2000 = 0
factoring:
(x-40)(x+50) = 0
x = {-50, 40}
since a negative doesn't make sense, the only solution is the positive one.
x = 40 mph
.
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