SOLUTION: A and B working together can do a job in 10 days. One takes 5 days less than the other to do the job when each works alone. How many days would it take each of them working alone t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A and B working together can do a job in 10 days. One takes 5 days less than the other to do the job when each works alone. How many days would it take each of them working alone t      Log On


   

Question 987576: A and B working together can do a job in 10 days. One takes 5 days less than the other to do the job when each works alone. How many days would it take each of them working alone to do the job?
P.S.: My math teacher said that the answer to this question is radicals
Thank you
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Lets assume a can do 1/A of the job in a day. and B can do 1/B of the job in a day.
You are told
1+=+10%2A%28%281%2FA%29+%2B+%281%2FB%29%29
0.1+=+%28B%2BA%29%2FAB
0.1AB+=+B%2BA
You are also told that A can do the job in X days. B takes X+5 days
1+=+%281%2FA%29X
A=X
1+=+%281%2FB%29%28X%2B5%29
B+=+X%2B5
Now plug those values for A and B into the equation above
0.1%28X%29%28X%2B5%29+=+X+%2B+%28X%2B5%29
0.1X%5E2+%2B+0.5X+=+2X+%2B+5
0.1X%5E2+-1.5X+-+5+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.1x%5E2%2B-1.5x%2B-5+=+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=%28-1.5%29%5E2-4%2A0.1%2A-5=4.25.

Discriminant d=4.25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1.5%2B-sqrt%28+4.25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1.5%29%2Bsqrt%28+4.25+%29%29%2F2%5C0.1+=+17.8077640640442
x%5B2%5D+=+%28-%28-1.5%29-sqrt%28+4.25+%29%29%2F2%5C0.1+=+-2.80776406404415

Quadratic expression 0.1x%5E2%2B-1.5x%2B-5 can be factored:
0.1x%5E2%2B-1.5x%2B-5+=+0.1%28x-17.8077640640442%29%2A%28x--2.80776406404415%29
Again, the answer is: 17.8077640640442, -2.80776406404415. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.1%2Ax%5E2%2B-1.5%2Ax%2B-5+%29


so A take 17.8 days and B takes 22.8 days by themselves