Thread: 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.

Hello, imbadatmath!


Recall the formula: .

We will use the variation: .

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 = her average speed.

She rode 300 miles at mph.
. . This took her: . hours.

If her speed were mph,
. . it would have taken her: . hours.

And this time is one hour less.

There is our equation . . .


Multiply by

. . which simplifies to: .


Go for it!