# Applications Involving Quadratic Equations

• April 24th 2008, 06:15 PM
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.
• April 24th 2008, 09:33 PM
Soroban

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

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

Quote:

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!