Answer
$10$ hours
Work Step by Step
Say the new copier needs x hours to complete the job, working alone.
In 1 hour,
the new copier does $\displaystyle \frac{1}{x}$ of the full job,
the older copier does $\displaystyle \frac{1}{x+5}$ of the full job,
In 6 hours, together they complete $( \displaystyle \frac{6}{x}+\frac{6}{x+5} )$ of the job,
which, by the text, is $\displaystyle \frac{1}{1},$ the whole job.
$\displaystyle \frac{6}{x}+\frac{6}{x+5}=1\qquad$
... LCD=$x(x+5)$
... multiply with $x(x+5)$
$6(x+5)+6x=x(x+5)$
$ 6x+30+6x=x^{2}+5x\qquad$... add $-12x-30$
$0=x^{2}-7x-30$
... two factors of -30 whose sum is -7
... are -10 and +3
$0=(x-10)(x+3)$
... x=10 or x=-3
... negative time makes no sense, so we discard that solution.
$x$ = $10$ hours.
