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:

`(1)/(t_1)+(1)/(t_2)=(1)/(t)`

Given:

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

Therefore,

`\begin{gathered} (1)/(4)+(1)/(t_2)=(1)/(3) \\ (1)/(t_2)=(1)/(3)-(1)/(4) \\ (1)/(t_2)=(4-3)/(12)=(1)/(12) \\ (1)/(t_2)=(1)/(12) \\ Cross\text{ multiply} \\ 1*12=1* t_2 \\ 12=t_2 \\ \therefore t_2=12 \end{gathered}`

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