SOLUTION: working together, linda and kathy can clean a beach house in 5.14 hours. had she done it alone it would have taken linda 11 hours. how long would it take kathy to do it alone?

Question 926052: working together, linda and kathy can clean a beach house in 5.14 hours. had she done it alone it would have taken linda 11 hours. how long would it take kathy to do it alone?
How do i set this problem up?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = linda work rate
y = kathy work rate
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rate = work/time
time = work/rate
work = 1 job (clean one house)
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x = 1/11
x + y = 1/5.14
1/11 + y = 1/5.14
y = 1/5.14 - 1/11
---
answer:
time for kathy working alone = work/rate
1/y = 1/( 1/5.14 - 1/11 )
1/y = 9.65 hours
---
check:
x + y = 1/5.14
1/11 + (1/5.14 - 1/11) = 1/5.14
5.14/(11*5.14) + ( 11/(11*5.14) - 5.14/(11*5.14) ) = 1/5.14
5.14/(11*5.14) + 11/(11*5.14) - 5.14/(11*5.14) = 1/5.14
11/(11*5.14) = 1/5.14
1/5.14 = 1/5.14
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