Daniel can encode a paper in $5$ hours and together he and Dennis can encode it in $2$ hours, how long would it take Dennis to encode the same paper alone?
If Daniel can encode a paper in $5$ hours, then he encodes $\frac15$th paper per hour. Let $n$ be the time it takes Dennis to encode a paper. $$\frac{1}{5} +\frac{ 1}{n} = \frac{1}{2}$$ $$2n + 10 = 5n$$ $$10 = 3n$$ $$n = \frac{10}{3}$$ $$n = 3\dfrac{1}{3}$$
They simply used ::$$\frac{1}{5}+\frac{1}{n}=\frac{1}{2}$$ $$\frac{5+n}{5n}=\frac{1}{2}$$ $$10+2n=5n\tag{basics of fraction addition}$$