SOLUTION: Jane and Maria can clean the house in 8 hours if they work together. The time Jane takes in cleaning the house alone is 4 hours more than the time Maria takes in cleaning the same

Question 889922: Jane and Maria can clean the house in 8 hours if they work together. The time Jane takes in cleaning the house alone is 4 hours more than the time Maria takes in cleaning the same house. How long does it take Jane to clean the house alone?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Jane and Maria can clean the house in 8 hours if they work together. The time Jane takes in cleaning the house alone is 4 hours more than the time Maria takes in cleaning the same house. How long does it take Jane to clean the house alone?
***
let x=hrs marie takes in cleaning the house alone
1/x=her work rate
x+4=hrs jane takes in cleaning the house alone
1/(x+4)=her work rate
Jane and Maria can clean the house in 8 hours if they work together.
1/8=their work rate
..
sum of indv. work rates=work rate working together

lcd:x(x+4)
x+4+x=(x^2+4x)/8
16x+32=x^2+4x
x^2-12x-32=0
solve for x by quadratic formula:
x≈-2.56 (reject)
or
x≈14.25
x+4≈18.25
How long does it take Jane to clean the house alone? 18.25 hrs
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