Sam and Wilson can paint a house together in 6 days. They painted the house together for 5 days and then Sam completed the painting of the remaining house alone in 3 days. How many days would it take for Wilson to paint the entire house by himself? Answer ... days

1. Find the fraction of the house completed together and the remaining fraction.

Sam and Wilson together paint the whole house in $6$ days.

Their combined rate is $\dfrac{1}{6}$ house per day.

In $5$ days, they paint
$5 \times \dfrac{1}{6}=\dfrac{5}{6}$
of the house.

Remaining work:
$1-\dfrac{5}{6}=\dfrac{1}{6}$

2. Find Sam's painting rate from the remaining work completed alone.

Sam completes the remaining $\dfrac{1}{6}$ of the house in $3$ days.

So Sam's rate is
$\dfrac{1}{6}\div 3=\dfrac{1}{18}$
house per day.

3. Find Wilson's rate and convert it to the time needed for the whole house.

Combined rate $=$ Sam's rate $+$ Wilson's rate.

Wilson's rate is
$\dfrac{1}{6}-\dfrac{1}{18}=\dfrac{3}{18}-\dfrac{1}{18}=\dfrac{2}{18}=\dfrac{1}{9}$
house per day.

Therefore Wilson would take
$1\div \dfrac{1}{9}=9$
days.