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?
:
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.
:
{{{10/d}}} + {{{10/((d-2))}}} = 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:
{{{10/21.05}}} + {{{10/19.05}}} ~ 1