SOLUTION: Tyrone and Lance can clean the house in 8 hours if they work together.If it takes Tyrone 4 hours more to clean the house compared to Lance, how long does it take Tyrone to clean th

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Question 890174: Tyrone and Lance can clean the house in 8 hours if they work together.If it takes Tyrone 4 hours more to clean the house compared to Lance, how long does it take Tyrone to clean the house alone? How about Lance?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Tyrone and Lance can clean the house in 8 hours if they work together.If it takes Tyrone 4 hours more to clean the house compared to Lance, how long does it take Tyrone to clean the house alone? How about Lance?
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let x=hours Lance can clean the house alone
1/x=his work rate
x+4=hours Tyrone can clean the house alone
1/(x+4)=his work rate
8=hours Lance and Tyrone can clean the house working together
1/8=their work rate
..
sum of individual work rates=work rate working together
1%2Fx%2B1%2F%28x%2B4%29=1%2F8
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≈-2.24 (reject)
or
x≈14.25
x+4≈18.25
hours Tyrone can clean the house alone=18.25
hours Lance can clean the house alone=14.25