Question 128327
All this says is that if you take any 2 people who are
able to do a certain job, one of them usually works
faster than the other, but if you are able to put
both of them to work on the same job, then they will
get it done faster than even the faster person
could do it alone.
In words,
(Anton's rate of working) + (Bill's rate of working) =
(their rate of working together)
And in more exact words,
{1 patio)/(Anton's time) + (1 patio)/(Bill's time) =
(1 patio)/ (their times working together)
Now with numbers:
Let {{{A}}} = Anton's time working alone
Let {{{B}}} = Bill's time working alone
{{{A = B - 2}}}
{{{1/A + 1/B = 1/4}}}
multiply both sides of the equation by {{{4AB}}}
{{{4B + 4A = AB}}}
{{{4B + 4(B - 2) = (B - 2)*B}}}
{{{4B + 4B - 8 = B^2 - 2B}}}
{{{B^2 - 10B + 8 = 0}}}
complete the square
{{{B^2 - 10B + 25 = -8 + 25}}}
{{{B - 5)^2 = 17}}}
{{{B - 5 = sqrt(17)}}}
{{{B = sqrt(17) + 5}}}
{{{B = 9.123}}}
The other solution is
{{{B = -sqrt(17) + 5}}} since there are 2 square roots (+) and (-)
{{{B = .877}}}
The larger  number is the only one that makes sense
Bill takes 9.1 hours working alone
check answer:
{{{A = B - 2}}}
{{{A = 9.123 - 2}}}
{{{A = 7.123}}}
{{{1/7.123 + 1/9.123 = 1/4}}}
{{{.14039 + .10961 = .25}}}
{{{.250003 = .25}}} close enough