Hello, tigerpawz74!
This is a "Work" problem . . . it requires special treatment.
Sally can paint a house in 4 hours, John can paint a house in 6 hours.
How long does it take them to paint the house together?
Here's the reasoning behind the set-up . . .
Sally can paint a house in 4 four hours.
\(\displaystyle \;\;\;\)In one hour, she can paint \(\displaystyle \frac{1}{4}\) of the house.
\(\displaystyle \;\;\;\)In \(\displaystyle x\) hours, she can paint \(\displaystyle \frac{x}{4}\) of the house.
John can paint the house in 6 hours.
\(\displaystyle \;\;\;\)In one hour, he can paint \(\displaystyle \frac{1}{6}\) of the house.
\(\displaystyle \;\;\;\)In \(\displaystyle x\) hours, he can paint \(\displaystyle \frac{x}{6}\) of the house.
Together, in \(\displaystyle x\) hours, they can paint: \(\displaystyle \frac{x}{4}\,+\,\frac{x}{6}\) of the house.
But in \(\displaystyle x\) hours, we expect them to paint
the whole house (\(\displaystyle 1\) house), right?
Well, <u>there</u> is our equation! \(\displaystyle \L\;\frac{x}{4}\,+\,\frac{x}{6}\:=\:1\)
