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=(1)/(5)h`

It takes Amelie 10 hours to paint the same room:

`y=(1)/(10)h`

The total will be:

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