Answer
$12$ hours
Work Step by Step
Say that I need x hours to finish the job on my own.
In 1 hour, I do $\displaystyle \frac{1}{x}$ of the full job, and
my cousin does $\displaystyle \frac{1}{4}$ of the full job.
In 3 hours , we complete $(\displaystyle \frac{3}{x}+\frac{3}{4})$ of the job.
The text says that this is $\displaystyle \frac{1}{1}$ of the job (the whole job).
$\displaystyle \frac{3}{x}+\frac{3}{4}=1\qquad$...multiply with $4x$
$ 12+3x=4x\qquad$... subtract $3x$
$12=x$
$x$= $12$ hours.
