Answer
$20$ hours.
Work Step by Step
Say the experienced bricklayer needs x hours to complete the job, working alone.
Then, the apprentice needs $x+10$ hours.\\\\
In 1 hour,
the bricklayer does $\displaystyle \frac{1}{x}$ of the full job,
the apprentice does $\displaystyle \frac{1}{x+10}$ of the full job,
In 12 hours, together they complete $( \displaystyle \frac{12}{x}+\frac{12}{x+10} )$ of the job,
which, by the text, is $\displaystyle \frac{1}{1},$ the whole job.
$\displaystyle \frac{12}{x}+\frac{12}{x+10}=1\qquad$
... LCD=$x(x+10)$
... multiply with $x(x+10)$
$12(x+10)+12x=x(x+10)$
$ 12x+120+12x=x^{2}+10x\qquad$... add $-24x-120$
$0=x^{2}-14x-120$
... two factors of $-120$ whose sum is $-14$
... are $-20$ and $+6$
$0=(x-20)(x+6)$
... $x=20$ or $x=-3$
... negative time makes no sense, so we discard that solution.
$x$ = $20$ hours.
