SOLUTION: Connie can type 600 words in 5 minutes less than it takes Katie to type 600 words. If Connie types at a rate of 20 words per minute faster than Katie types, find the rate of each w

Algebra ->  Graphs -> SOLUTION: Connie can type 600 words in 5 minutes less than it takes Katie to type 600 words. If Connie types at a rate of 20 words per minute faster than Katie types, find the rate of each w      Log On


   

Question 171115: Connie can type 600 words in 5 minutes less than it takes Katie to type 600 words. If Connie types at a rate of 20 words per minute faster than Katie types, find the rate of each woman.

I need help please!
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call kates time t and her rate r
lets call connies time t-5 and her rate r+20
words typed are equal.
:
600=rt.......eq 1
600=(r+20)(t-5)..eq 2
:
lets rewrite eq 1...t=600/r and plug that value into eq 2
:
600=%28r%2B20%29%28%28600%2Fr%29-5%29---->600=%28r%2B20%29%28%28600-5r%29%2Fr%29...multiply by r
:
600r=%28r%2B20%29%28600-5r%29--->600r=600r-5r%5E2%2B12000-100r
:
5r%5E2%2B100r-12000=0divide by 5
r%5E2%2B20r-2400=0
:
throw out the negative numbersystem%28r=40%2Cr=-60%29
:
so highlight%28r=40%29WPM kates typing speed
:highlight%28r%2B20%29WPM connies typing speed

:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B20x%2B-2400+=+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=%2820%29%5E2-4%2A1%2A-2400=10000.

Discriminant d=10000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-20%2B-sqrt%28+10000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+10000+%29%29%2F2%5C1+=+40
x%5B2%5D+=+%28-%2820%29-sqrt%28+10000+%29%29%2F2%5C1+=+-60

Quadratic expression 1x%5E2%2B20x%2B-2400 can be factored:
1x%5E2%2B20x%2B-2400+=+1%28x-40%29%2A%28x--60%29
Again, the answer is: 40, -60. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B20%2Ax%2B-2400+%29