3. Working together, Jack and Jill can paint a house in 3 days; Jill and Joe can paint the same house in 4 days; or Joe and Jack can paint the house in 6 days. If Jill, Joe, and Jack all work together, how many days will it take them?
Solution: $8 / 3$
Suppose that Jack paints $x$ houses per day, Jill paints $y$ houses per day, and Joe paints $z$ houses per day. Together, Jack and Jill paint $1 / 3$ of a house in a day - that is,
$$
x+y=1 / 3 \text {. }
$$

Similarly,
$$
y+z=1 / 4,
$$
and
$$
z+x=1 / 6 .
$$

Adding all three equations and dividing by 2 gives
$$
x+y+z=3 / 8 .
$$

So, working together, the three folks can paint $3 / 8$ houses in a day, or $8 / 3$ days per house.