Answer
$18\;\rm hp$
Work Step by Step
We know that the power is given by
$$P=Fv$$
We know that the power to tow a water skier at a speed of 2.5 mph is about 2 hp.
In our case, we know that the tow force is given by $F_{tow}=Av$
$$P_{tow}=(Av)v=Av^2$$
And to find the power to tow the same skier at speed of 7.5 mph, we need to find the proportionality constant $A$.
Thus,
$$A=\dfrac{P_{tow,1}}{v^2_1}$$
Plugging the known;
$$A=\dfrac{2}{2.5^2 }=\bf 0.32\;\rm hp/(mph)^2$$
Now we can easily find the power needed at speed of 7.5 mph.
$$P_{tow,2}= Av_2^2$$
Plugging the known;
$$P_{tow,2}=0.32\times 7.5^2$$
$$P_{tow,2}=\color{red}{\bf 18}\;\rm hp$$
