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Math Help - Applications Involving Quadratic Equations

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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: . \text{[Distance]} \:=\:\text{[Speed]} \times \text{[Time]}

    We will use the variation: . 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 x = her average speed.

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

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

    And this time is one hour less.

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


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

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


    Go for it!

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