Question 164391
Melanie's rate + Mellisa's rate = rate working together 
(1 barn / x days + 1 barn / 2x days)
As an algebra expression:
{{{1/x + 1/2x}}}
{{{x = 5}}}
{{{1/5 + 1/10 = 2/10 + 1/10}}}
{{{2/10 + 1/10 = 3/10}}}
What this says is that they can paint 3 barns in 10 days
by working together, but there is only 1 barn to paint.
I'll make a new quantity called {{{y}}} and I'll write
{{{1/y = 3/10}}} This says (1 barn/y days) = (3 barns/10 days)
Solve for {{{y}}} by multiplying both sides by {{{10y}}}
{{{10 = 3y}}}
{{{y = 10/3}}}
So, working together, they can paint 1 barn in {{{10/3}}} days