Question 206592: I know rate times time equals distance, but I'm still confused. 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.
Answer by Theo(13342)   (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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let x = the certain speed in miles per hour.
let h = the time it took in hours.
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rate * time = distance becomes x * h = 200
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if he had gone 10 mph faster his rate would have been 10 mph more than whaqt it was which is the same as x + 10
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if he had gone 10 mph faster his time would have been 1 hour less which is the same as h - 1
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solve for x
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you have 2 equations.
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the first equation is x * h = 200
the second equation is (x+10)*(h-1) = 200
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since both equations are equal to 200 then they are equal to each other.
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your equation becomes:
x*h = (x+10)*(h-1)
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if you multiply this out you get h^2 - h - 20 = 0 which factors out to be (h-5) * (h+4) = 0 which makes h = 5 or h = -4.
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since h = -4 is not possible your answer has to be be h = 5
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if you substitute 5 for h in your first equation you get 5x = 200 which makes x = 40
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your answer should be:
x = 40 = speed he traveled at.
h = 5 = number of hours it took.
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5*40 = 200 so this part checks out.
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second part states if he went 10 mph faster he would have taken 1 hour less.
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10 mph faster would be 50 mph.
1 hour less would be 4 hours.
50 * 4 = 200 so this part checks out also.
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answer is his original rate of travel was 40 miles per hour and the original time it took was 5 hours.
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