Answer
$400$ ft-lb
Work Step by Step
We know that Hooke's Law states that $F=k x$
and work $=force \times distance$ or, $W=Fd$
Here, the water weight $=2(20-x)$
To calculate the work done, the limits for $x$ will be from $0$ to $20$ such that:
$W=\int_0^{20} (2(20-x)) dx=\int_0^{20} (40-2x) dx=[40x-x^2]_0^{20}$
or, $W=[40(20-0)-(400-0)]=800-400=400$ ft-lb
