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Thread: Applications Involving Quadratic Equations

  1. #1
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    Applications Involving Quadratic Equations

    Madison rode her motorcycle 300 miles at a certain average speed. Had she averaged 10 miles per hour more, the trip would have taken 1 hour less. Find the average speed of the motorcycle.
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  2. #2
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    Hello, imbadatmath!


    Recall the formula: .$\displaystyle \text{[Distance]} \:=\:\text{[Speed]} \times \text{[Time]} $

    We will use the variation: .$\displaystyle T \:=\:\frac{D}{S}$


    Madison rode her motorcycle 300 miles at a certain average speed.
    Had she averaged 10 miles per hour more, the trip would have taken 1 hour less.
    Find the average speed of the motorcycle.
    Let $\displaystyle x$ = her average speed.

    She rode 300 miles at $\displaystyle x$ mph.
    . . This took her: .$\displaystyle \frac{300}{x}$ hours.

    If her speed were $\displaystyle x+10$ mph,
    . . it would have taken her: .$\displaystyle \frac{300}{x+10}$ hours.

    And this time is one hour less.

    There is our equation . . . $\displaystyle \frac{300}{x+10} \;=\;\frac{300}{x} - 1$


    Multiply by $\displaystyle x(x+10)\!:\;\;300x \;=\;300(x+10) - x(x+10)$

    . . which simplifies to: .$\displaystyle x^2 + 10x - 3000 \:=\:0$


    Go for it!

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