Answer
The number of days that Mr. Crocker and his son needed to complete the paint job of the shed together is $1\frac{5}{7}$ days.
Work Step by Step
Let $x$ be the number of days that both of them needed to complete the job together and $W$ be the entire paint work of the shed to be completed
Since Mr. Crocker can paint the shed by himself in three
days, the work that he can complete in 1 day is $\frac{1}{3}W$
And, for his son, an additional day is needed to complete
the job if he works alone, so, the work his son can complete in 1 day is $\frac{1}{4}W$
Now, if they work together, the work they can complete in 1 day is $\frac{1}{3}W$ + $\frac{1}{4}W$, and therefore,
$(\frac{1}{3}W$ + $\frac{1}{4}W) \cdot x = W$
$(\frac{4}{12}W$ + $\frac{3}{12}W) \cdot x = W$ (LCD = 12)
$(4 + 3) \cdot x = 12$
$7x = 12$
$x = \frac{12}{7}$
$x = 1\frac{5}{7}$
The number of days that Mr. Crocker and his son needed to complete the paint job of the shed together is $1\frac{5}{7}$ days.
