SOLUTION: 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.

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Question 107752This question is from textbook intermediate algebra
: 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. This question is from textbook intermediate algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.
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1st speed DATA:
distance = 200 miles; rate = x mph ; time = d/r = 200/x hrs
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2nd speed DATA;
distance = 200miles ; rate = x+10 mph ; time = d/r = 200/(x+10)
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EQUATION:
1st time - 2nd time = 1 hr
200/x - 200/(x+10) = 1
1/x - 1/(x+1) = 1/200
[x+1-x]/x(x+1) = 1/200
1/[x(x+1)] = 1/200
x(x+1) = 200
x^2+x-200=0
x = [-1 +- sqrt(1 - 4*-200)]/2
x = [-1 +- sqrt(801)]/2
x = 13.65 mph (speed of his vehicle)
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Cheers,
Stan H.