Answer
$160 ft-lb$
Work Step by Step
Hooke's Law states that $F=k x$
and Work $=force \times distance$ or, $W=Fd$
The water weight is found as: $=16-(\dfrac{4}{5}) x$
Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$
This implies that
$W=\int_0^{(20)} [16-(\dfrac{4}{5}) x] dx=[(16x -\dfrac{4}{5}(\dfrac{x^{1+1}}{1+1}))]_0^{20}$
Hence, $W=[(16x -\dfrac{4}{5}(\dfrac{x^{2}}{2}))]_0^{(20)}=[16(20-0)-\dfrac{2}{5}(400-0)]=320-160=160 ft-lb$
