Question

Jean can paint a room in 5 hours. It takes Amelie 10 hours to paint the same room. How many hours will it take if they work together?

Answer 1

$\begin{gathered} Let\colon \\ x=\text{ rate of work of Jean} \\ y=\text{ rate of work of Amelie} \\ T=\text{ Total hours if they work together} \end{gathered}$

Jean can paint a room in 5 hours, so:

$x=\frac{1}{5}h$

It takes Amelie 10 hours to paint the same room:

$y=\frac{1}{10}h$

The total will be:

$\begin{gathered} \frac{1}{10}+\frac{1}{5}=\frac{1}{T} \\ \text{ Multiply both sides by 10:} \\ 1+2=\frac{10}{T} \\ 3=\frac{10}{T} \\ \text{ Multiply both sides by T:} \\ 3T=10 \\ \text{Divide both sides by 3:} \\ T=\frac{10}{3}\approx3.33h\text{ } \\ \end{gathered}$$\text{rate of work=}\frac{job}{hours}$