Question

Patrick takes 8 hours to paint his room. After working for 1 hour, he called in a painter to help him. Working together, they finish the job in 3 more hours. How long would it take the painter to finish the job if he had worked alone?

Answer 1

\(\large \begin{align} \color{black}{\normalsize \text{patrick}\rightarrow 8 ~hrs\hspace{.33em}\\~\\

\normalsize \text{patrick after working for 1 hour called the painter }\hspace{.33em}\\~\\
\normalsize \text{patrick and painter took 3 more hours means}\hspace{.33em}\\~\\
\normalsize \text{they finished it in 4 hours }\hspace{.33em}\\~\\
\normalsize \text{patrick}+\text{painter}\rightarrow 4 ~hrs\hspace{.33em}\\~\\
\normalsize \text{let the work be of 8 units , so }\hspace{.33em}\\~\\
\normalsize \text{patrick}\rightarrow \dfrac{ 8 ~units}{8~hrs}=1~unit/hr\hspace{.33em}\\~\\
\normalsize \text{patrick}+\text{painter}\rightarrow \dfrac{8 ~units}{4~hrs}=2~unit/hr \hspace{.33em}\\~\\
\normalsize \text{let painter takes x hrs alone , so }\hspace{.33em}\\~\\
\normalsize \text{painter}\rightarrow \dfrac{8~units}{x~hrs }=8 ~unit/hr\hspace{.33em}\\~\\
1+\dfrac{8}{x}=2 \hspace{.33em}\\~\\
x=8~hrs
}\end{align}\)