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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 200%2F%28R%2B10%29=+%28200%2FR%29+-1
Multiply everything by (R+10)
200+=+200+%2B+2000%2FR+-+R+-+10 Combine like terms
200+=+190+%2B+2000%2FR+-+R
Multiply Everything by R
200R+=+190R+%2B+2000+-+R%5E2
Subtract 200R from both sides
0+=+-10R+%2B+2000+-+R%5E2
Use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B-10x%2B2000+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-10%29%5E2-4%2A-1%2A2000=8100.

Discriminant d=8100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+8100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+8100+%29%29%2F2%5C-1+=+-50
x%5B2%5D+=+%28-%28-10%29-sqrt%28+8100+%29%29%2F2%5C-1+=+40

Quadratic expression -1x%5E2%2B-10x%2B2000 can be factored:
-1x%5E2%2B-10x%2B2000+=+-1%28x--50%29%2A%28x-40%29
Again, the answer is: -50, 40. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-10%2Ax%2B2000+%29


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.