How did they get 2n + 10 here?

Question

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. $$\frac{1}{5} +\frac{ 1}{n} = \frac{1}{2}$$ $$2n + 10 = 5n$$ $$10 = 3n$$ $$n = \frac{10}{3}$$ $$n = 3\dfrac{1}{3}$$

Since $n\neq 0$, have you tried to multiply both sides of the equation by 10n? — Ender Wiggins, May 06 '17 at 09:14

score 2 · Accepted Answer · answered May 06 '17 at 09:15

2

They simply used ::$$\frac{1}{5}+\frac{1}{n}=\frac{1}{2}$$ $$\frac{5+n}{5n}=\frac{1}{2}$$ $$10+2n=5n\tag{basics of fraction addition}$$

answered May 06 '17 at 09:15

The Dead Legend

4,727

Genius, thanks for the help. What do you call this process sir? – Allan Chua May 06 '17 at 09:16
Uh, simply making the denominator same? and then adding. No name required – The Dead Legend May 06 '17 at 09:17
@AllanChua see this: https://www.mathsisfun.com/fractions_addition.html – The Dead Legend May 06 '17 at 09:17

How did they get 2n + 10 here?

1 Answers1