We know that the time is inversely proportional to the work.
Let t₁ is the time taken by Jeff and t₂ is the time taken by Jeff's dad.
We know that the formula:
[tex]\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{t}[/tex]Given:
[tex]\begin{gathered} t_1=4hours \\ t_2=? \\ t=3hours \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{1}{4}+\frac{1}{t_2}=\frac{1}{3} \\ \frac{1}{t_2}=\frac{1}{3}-\frac{1}{4} \\ \frac{1}{t_2}=\frac{4-3}{12}=\frac{1}{12} \\ \frac{1}{t_2}=\frac{1}{12} \\ Cross\text{ multiply} \\ 1\times12=1\times t_2 \\ 12=t_2 \\ \therefore t_2=12 \end{gathered}[/tex]Hence, it took Jeff's dad 12hours to wash the car himself.
