Answer
$16 \text{ pounds}$
Work Step by Step
The variation model described by the problem is $
F=kAs
,$ where $F$ is the force, $A$ is the surace area, and $s$ is the speed.
Substituting the known values of the variables results to
\begin{array}{l}\require{cancel}
20=k(12)(10)
\\
20=120k
\\
\dfrac{20}{120}=k
\\\\
k=\dfrac{\cancel{20}}{\cancel{20}\cdot6}
\\\\
k=\dfrac{1}{6}
.\end{array}
Hence, the equation of variation is
\begin{array}{l}\require{cancel}
F=\dfrac{1}{6}As
.\end{array}
Using the variation equation above, then
\begin{array}{l}\require{cancel}
F=\dfrac{1}{6}As
\\\\
F=\dfrac{1}{6}(8)(12)
\\\\
F=\dfrac{1}{\cancel6}(8)(\cancel6\cdot2)
\\\\
F=16
.\end{array}
Hence, the force, $F,$ is $
16 \text{ pounds}
.$
