Question

A painting contractor knows from experience that sanding trim requires 0.80-1.00 hours of labor per 100 linear feet, and that staining that same trim requires 0.50-0.75 hours of labor per 100 linear feet. What would be the minimum and maximum number of total hours of labor required for sanding and staining 360 linear feet of trim? (Round each answer to the nearest half-hour.

Answer 1

It is given that the sanding trim requires 0.80-1.00 hours per 100 linear feet.

So the minimum and maximum values for sanding 360 linear feet is given by:

$\begin{gathered} S_{\min }=0.80\times\frac{360}{100}=2.88 \\ S_{\max }=1\times\frac{360}{100}=3.6 \end{gathered}$

Hence the maximum and minimum time for sanding is 3.6 and 2.88 hours respectively.

It is also given that the staining requires 0.5-0.75 hours of labor. So the staining denoted by T for 360 feet will be:

$\begin{gathered} T_{\min }=0.5\times\frac{360}{100}=1.8 \\ T_{\max }=0.75\times\frac{360}{100}=2.7 \end{gathered}$

Hence the minimum and maximum time for staining is 1.8 and 2.7 hours respectively.

So the total minimum and maximum time is given by:

$\begin{gathered} T^{\prime}_{\min }=S_{\min }+T_{\min }=2.88+1.8=4.68 \\ T^{\prime}_{\max }=S_{\max }+T_{\max }=3.6+2.7=6.3 \end{gathered}$

Hence the total minimum time is 4.68 hours and the total maximum time is 6.3 hours.