Question 231969
If you're evaluating this for x=5, put the 5 in for the x's to give you the following rational expression:

1/5 + 1/(2*5) = 1/x

You only want one variable, x.

So assign x as the part of the barn they can paint together.

It takes melanie 5 days, so for one days work the fraction is 1/5.

It takes Sara twice as long, so 10 days.  her work for 1 day is 1/10.

You don't know how long it will take them working together, so that portion is x

So you get the following equation:

1/5 + 1/10 = 1/x

The LCD is 10x, so multiply everything by 10x to give you:

2x + x = 10

Add like terms:

3x = 10

Divide both sides by 3:

x = 3 1/3 days

So it will take 3 and 1/3 days for them both working together to paint the barn.  

You can check this by putting 3 1/3 in for x in our equation.

Hope this helps!