山姆和威尔逊合作粉刷一间房子需要6天。他们一起粉刷了5天，然后山姆独自一人用3天时间完成了剩下部分的粉刷。如果让威尔逊独自一人粉刷整间房子，需要多少天？ 答案 ... 天

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.