SOLUTION: If the distance traveled is 5x^3 - 6x^2+3x+14 miles and the rate is x+1 per hour, what is the time traveled? Thank you!

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Question 130123: If the distance traveled is 5x^3 - 6x^2+3x+14 miles and the rate is x+1 per hour, what is the time traveled?
Thank you!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the formula d=r%2At

d=r%2At Start with the given formula


5x%5E3+-+6x%5E2%2B3x%2B14=%28x%2B1%29%2At Plug in d=5x%5E3+-+6x%5E2%2B3x%2B14 and r=x%2B1


%285x%5E3+-+6x%5E2%2B3x%2B14%29%2F%28x%2B1%29=t Divide both sides by x%2B1


%28%28x%2B1%29%285x%5E2+-+11x+%2B+14%29%29%2F%28x%2B1%29=t Factor 5x%5E3+-+6x%5E2%2B3x%2B14 to get %28x%2B1%29%285x%5E2+-+11x+%2B+14%29 (note: you can use a graphing calculator to help you do this)


%28cross%28x%2B1%29%285x%5E2+-+11x+%2B+14%29%29%2Fcross%28x%2B1%29=t Cancel like terms


5x%5E2+-+11x+%2B+14=t Simplify


So the time is

t=5x%5E2+-+11x+%2B+14

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If the distance traveled is 5x^3 - 6x^2+3x+14 miles and the rate is x+1 per hour, what is the time traveled?
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Time = d/r
Use synthetic division to divide:
-1....5....-5....3....14
.......5.....-10...13..|..1
Quotient: 5x^2-10x+13
Remainder: 1
Time = 5x^2-10x+13 + 1/(x+1)
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Cheers,
Stan H.