Question

Washing his dad's car alone, Jeff takes 4 hours. If his dad helps him, then it takes 3 hours. How long does it take Jeff's dad to wash the car by himself?

Answer 1

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:

$\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{t}$

Given:

$\begin{gathered} t_1=4hours \\ t_2=? \\ t=3hours \end{gathered}$

Therefore,

$\begin{gathered} \frac{1}{4}+\frac{1}{t_2}=\frac{1}{3} \\ \frac{1}{t_2}=\frac{1}{3}-\frac{1}{4} \\ \frac{1}{t_2}=\frac{4-3}{12}=\frac{1}{12} \\ \frac{1}{t_2}=\frac{1}{12} \\ Cross\text{ multiply} \\ 1\times12=1\times t_2 \\ 12=t_2 \\ \therefore t_2=12 \end{gathered}$

Hence, it took Jeff's dad 12hours to wash the car himself.