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.
Hello, imbadatmath!
Recall the formula: .$\displaystyle \text{[Distance]} \:=\:\text{[Speed]} \times \text{[Time]} $
We will use the variation: .$\displaystyle T \:=\:\frac{D}{S}$
Let $\displaystyle x$ = her average speed.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.
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!