SOLUTION: Working alone, peter can paint a house in 2h less than Daniel. Working together, they can paint the house in 10h. How long would it take Daniel to paint the house by himself?

Question 766879: Working alone, peter can paint a house in 2h less than Daniel. Working together, they can paint the house in 10h. How long would it take Daniel to paint the house by himself?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Working alone, peter can paint a house in 2h less than Daniel.
Working together, they can paint the house in 10h.
How long would it take Daniel to paint the house by himself?
:
let d = time required by Daniel alone
then
(d-2) = Peter's time alone
:
Let the completed job = 1, each will do a fraction of the job, the two fractions add up to 1.
:
+ = 1
multiply by d(d-2) to clear the denominators, resulting in"
10(d-2) + 10d = d(d-2)
10d - 20 + 10d = d^2 - 2d
combine as a quadratic equation on the right
0 = d^2 - 2d - 20d + 20
d^2 - 22d + 20
This will not factor, use the quadratic formula to find the reasonable answer
I got d = 21.05 hrs, Daniels time alone
:
:
:
Check this out using a calc:
+ ~ 1

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