Answer
increases by $8$ times
Work Step by Step
The variation model described by the problem is $
H=ks^3
,$ where $H$ is the horsepower and $s$ is the speed of the boat.
If $s=1,$ then
\begin{array}{l}\require{cancel}
H_1=k(1)^3
\\
H_1=k
.\end{array}
If $s=2$ ($s$ is doubled), then
\begin{array}{l}\require{cancel}
H_2=k(2)^3
\\
H_2=k(8)
\\
H_2=8k
.\end{array}
Comparing $H_1$ and $H_2$, when $s$ is doubled, the horsepower increases by $8$ times.
