SOLUTION: Amy drove 200 miles to New Orleans at an average speed of 10 miles per hour faster than her usual speed. If she completed the trip in 1 hour less than usual, what is her usual dri

Question 305798: Amy drove 200 miles to New Orleans at an average speed of 10 miles per hour faster than her usual speed. If she completed the trip in 1 hour less than usual, what is her usual driving speed, in miles per hour.
Solve: 200/r+10 = (200/r)-1
Book says the answer is 40
How do you simplify the above equation and solve for 40?
Answer by Stitch(470) (Show Source): You can put this solution on YOUR website!
Given:
Multiply everything by (R+10)
Combine like terms

Multiply Everything by R

Subtract 200R from both sides

Use the quadratic equation

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=8100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -50, 40. Here's your graph:

The quadratic equation gives you two answers: -50, & 40. Since Amy could not have been driving at a negative rate, 40 is the only answer.
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